When we simplify the expression Logₐ1 + 3Logₐx - 2Logₐ4x, the result obtained is Logₐ (x/ 16)
How so i simplify the logarithm expression?The logarithm expression Logₐ1 + 3Logₐx - 2Logₐ4x can be simplified as illustrated below:
Expression: Logₐ1 + 3Logₐx - 2Logₐ4xSimplification =?Expression: Logₐ1 + 3Logₐx - 2Logₐ4x
Recall
mLog n = Lognᵐ
Thus, we have
Logₐ1 + 3Logₐx - 2Logₐ4x = Logₐ1 + Logₐx³ - Logₐ(4x)²
Logₐ1 + 3Logₐx - 2Logₐ4x = Logₐ1 + Logₐx³ - Logₐ16x²
Recall,
Log M + Log N = LogMN
Log M - Log N = Log (M/N)
Thus, we have
Logₐ1 + Logₐx³ - Logₐ16x² = Logₐ[(1 × x³) / 16x²]
Logₐ1 + Logₐx³ - Logₐ16x² = Logₐ(x³/ 16x²)
Logₐ1 + Logₐx³ - Logₐ16x² = Logₐ (x/ 16)
Thus,
Logₐ1 + 3Logₐx - 2Logₐ4x = Logₐ (x/ 16)
Therefore, we can conclude that the simplified expression of Logₐ1 + 3Logₐx - 2Logₐ4x, is Logₐ (x/ 16)
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Greg’s family went to the movie theater and bought tickets and popcorn. They spent $35 altogether with $9.50 spent on popcorn. Write an equation that can be used to find out how much money x they spent on tickets.
Answer:
x + 9.50 = 35
Step-by-step explanation:
The missing variable in this case is the number of dollars they spent on tickets. In total, combined the tickets and popcorn is equal to 35$,
We already know the amount they spent on popcorn.
X, the amount they spent on tickets + 9.50=35
El perímetro de un rectángulo es 36cm Uno de los lados es 6cm más que el otro lado ¿ Cual es el área del rectángulo?
Carlin pays $ 25 for her monthly phone service and $.02 for each minute m of talk time. Which expression represents her monthly bill?
A. 2m + 25 B. 25m + 0.02 C. .02m + 25 D. 25m + 2
Answer:
I think the answer B
If not then, sorry
The town of Passaic had 58,753 people in 1990 and 71,509 people in 2014.
PART A: Find the percent change in population. Explain/Show your
work.
PART B: Was it a percent increase or decrease? Explain how you know.
please help mee
Answer:
21.71% increase
Step-by-step explanation:
increase = Increase ÷ Original Number × 100
12756/58753*100
0.217112318*100
21.71% increase.
MARK ME BRAINLIEST
can anyone help me create 3 Algebra Word Problems
use greatest common factor and distributive property to write equivalent expressions 5x+20y
Answer:
I think it is 5 if I did it right
S
Subtract the following polynomials
1. (q² + 8) - (4q² + 1)
2. (3x + 7x² - 6) - (5x² + x + 9)
Answer:
1. (q² + 8) - (4q² + 1)
Simplify each term.
q²+8−4q²−1
Simplify by adding terms.
−3q²+7
2. (3x + 7x² - 6) - (5x² + x + 9)
Simplify each term.
3x+7x²−6−5x²−x−9
Simplify by adding terms.
Tap for more steps...
2x²+2x−15
Step-by-step explanation:
Find the missing part .
One coffee and two slices of cake cost 8 dollars in total. Two coffees and 3 slices of cake cost 14 dollars in total. What are the individual prices of one coffee and of one slice of cake?
Answer:
Step-by-step explanation:
coffee=c
cakes=d
c+2d=8
2c+3d=14
c=8-2d
2(8-2d)+3d=14
16-4d+3d=14
-d=-2
d=2
c+4=8
c=4
coffee=4 dollars each
cakes=2 dollars each
The price of coffee is $4 and price of slice of cake is $2.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
One coffee and two slices of cake cost 8 dollars in total.
Two coffees and 3 slices of cake cost 14 dollars in total.
let the price of coffees sold be x
let the price of slices of cake sold be y
Then, the system of equations are
x+ 2y = 8
2x+ 3y = 14
On solving
2(8- 2y)+ 3y= 14
16 - 4y + 3y= 14
-y= -2
y= 2
and, x = 8- 2(2)= 8- 4= 4
Hence, price of coffee is $4 and price of slice of cake is $2.
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Last year there were 80 members in chess club this year membership decreased by 20% how many members are there? Sorry
Answer:64 people
Step-by-step explanation: total no. of members=80
%decrease=20
20/100 x 80=16(people that left)
people rem.=80-16
Find the area. Simplify your answer.
Answer:
x = 26
Step-by-step explanation:
it is a right angle so
(x+4)3=90
3x+12=90
-12 -12
3x = 90-12
3x = 78
/3 /3
x = 26
please help me on this will give you brainliest
Answer:
7.76 × 10^8
Step-by-step explanation:
Answer:
i think i would be 1.94x10^8
Step-by-step explanation:
I don't remember how to do this question,
also I'm really sorry I keep posting alot of math stuff today, I just have a lot of math that needs to get done today, I'd rather not spend my whole weekend doing school work LOL
Answer:
x and p equal 92 and y equals 88
help help please!!!! thank youuu
Answer:
*Most of these, you just have to get the variable by itself. To check, put the answer in for the letter.*
1. b+8=14
Subtract 8 from both sides
b=6
Check: 6+8=14 ——— 14=14
2. 25-t=15
Subtract 25 from both sides
-t = -10 ––Divide both sides by -1
t=10
Check: 25-10=15 ——— 15=15
3. 9p=81
Divide both sides by 9 to get p alone
p=9
Check: 9(9)=81 ——— 81=81
4. y/7= 2
Multiply both sides by 7 to cancel out the fraction
y=14
Check: 14/7=2 ——— 2=2
5. y+6=10
Subtract 6 from both sides
y=4
Check: 4+6=10 ——— 10=10
6. f-4=9
Add 4 to both sides
f=13
Check: 13-4=9 ——— 9=9
7. 8d=48
Divide both sides by 8 to get d alone
d=6
Check: 8(6)=48 ——— 48=48
8. 10 = r/5
Multiply both sides by 5 to cancel out the fraction
50 = r
Check: 10=50/5 ——— 10=10
9. 15=x/3
Multiply by 3 to cancel out the fraction
45=x
Check: 15=45/3 ——— 15=15
Find the slope of a line that passes through the points (-1, -3) and (2, -2).
Answer:
Step-by-step explanation:
(-2 + 3)/(2 + 1) = 1/3 is the slope
PLS CAN SOMEONE HELP ME PLS
Answer:
20 m
Step-by-step explanation:
Let the length of the perpendicular dropped from vertex C to segment AB be x
By geometric mean property:
[tex]x = \sqrt{16 \times 9} \\ \\ x = \sqrt{144} \\ \\ x = 12 \: m \\ \\ By \: Pythagoras \: Theorem: \\ \\ Distance \: across \: the \: pond \\ \\ = \sqrt{ {16}^{2} + {12}^{2} } \\ \\ = \sqrt{256 + 144} \\ \\ = \sqrt{400} \\ \\ = 20 \: m[/tex]
Extra 13 points on this
Answer and Step-by-step explanation:
This graph is linear. The graph would look like this:
#teamtrees #WAP (Water And Plant) #PAW (Plant And Water)
#PAWG (Plant And Water Gang)
Line G has a slope of -2/3. Line age is perpendicular to G. What is the slope of line h?
Perpendicular lines has negative reciprocal slopes.
"Negative reciprocal" is just a fancy way of
saying flip the fraction and change the sign.
So flipping the fraction gives us -3/2 and change the sign to get +3/2.
Please help!!
Given f(x) = 3x-4 and g(x) = 2x+6 , find (fog)(x)
Answer:
[tex](f\circ g)(x)=6x+14[/tex]
Step-by-step explanation:
We are given the two functions:
[tex]f(x)=3x-4\text{ and } g(x)=2x+6[/tex]
And we want to find:
[tex](f\circ g)(x)[/tex]
This is equivalent to:
[tex]=f(g(x))[/tex]
Then by substitution:
[tex]=f(2x+6)=3(2x+6)-4[/tex]
Evaluate:
[tex]=f(g(x))=6x+18-4=6x+14[/tex]
Therefore:
[tex](f\circ g)(x)=6x+14[/tex]
The dimensions of a square are altered so that one dimension is increased by 7 feet, while the other is decreased by 2 feet. The are of the resulting rectangle is 90ft^2. Find the original area of the square.
Answer:
64 ft^2
Step-by-step explanation:
(x+7)(x-2)=90
x^2-2x+7x-14=90
x^2+5x-104=0
factor
(x+13)(x-8)=0
x=-13
x=8 ft original square side
area=8x8=64
Answer:
64 ft^2
Step-by-step explanation:
What is the value of x in the equation 4(2x + 12) = 0? a −8 b −6 c 6 d 8
Answer:
the answer is b:-6
Step-by-step explanation:
hoped I helped:)
Name the triangle
Please help fast
Answer:
B. Equilateral
It is an equilateral triangle
As we can see all sides are equal.
Equilateral Triangle
Step-by-step explanation:
PLEASE EXPLAIN HOW U DID IT, giving brainliest
9514 1404 393
Answer:
(b) 30
Step-by-step explanation:
The standard form of a quadratic is ...
y = ax^2 +bx +c
For such a function, the axis of symmetry is ...
x = -b/(2a)
Your quadratic function has a=-5, b=+300, so the axis of symmetry is ...
x = -300/(2(-5) = 30
The peak of the curve is on the axis of symmetry. So, profit is maximized when 30 items are produced.
_____
Of course, a graphing calculator can display the maximum of the function easily.
10 Points<>I need help ASAP!!!
Answer:
Step-by-step explanation:
A and D
Select all names that apply to the number 3/7
Answer:
WYM
Step-by-step explanation:
10 POINTS FOR WHOEVER ANWSERS!
Answer:
Infinitely many solutions
Step-by-step explanation:
Please I need the answer ASAP
Answer:
option C is correct answer of this question
Answer:
the answer is c 2 teaspoons
Step-by-step explanation:
if you divide 84 by 21 you would get 4. then you multiply 1/2 by 4 and get 2 teaspoons.
how to calculate perimeter
Answer:
To calculate perimeter add all the sides of the particular shape.
I hope this helps!
Square perimeter formula: P = 4a
Rectangle perimeter formula: P = 2(a + b)
Triangle perimeter formulas:
P = a + b + c or
P = a + b + √(a² + b² - 2ab * cos(γ)) or
P = a + (a / sin(β + γ)) * (sin(β) + sin(γ))
Circle perimeter formula: P = 2πr
Circle sector perimeter formula: P = r(α + 2) (α is in radians)
Ellipse perimeter formula: P = π(3(a + b) - √((3a + b) * (a + 3b)))
Quadrilateral / Trapezoid perimeter formula: P = a + b + c + d
Parallelogram perimeter formulas:
P = 2(a + b) or
P = 2a² + √(2e² + 2f² - 4a²) or
P = 2(b + h/sin(α))
Rhombus perimeter formulas:
P = 4a or
P = 2√(e² + f²)
Kite perimeter formula: P = 2(a + b)
Annulus perimeter formula: P = 2π(R + r)
Regular polygon area formula: P = n * a
verify that the segments are parallel
Answer:
We know that lines AB and CD are parallel because if you expand them, we know they will never touch.
Step-by-step explanation:
Please help me by solving this!
Answer:
Ani age is 21
Biju age is 18
Step-by-step explanation:
let Ani age be X
let Biju age be Y
the difference of their age is 3
i.e X - Y = 3......,....(equ. 1)
let Dharam age be A
let Cathy age be B
i.e A = 2x
B = y/2
the difference of their age is 30
Y/2 - 2x = 30..... (equ. 2)
from equ.1 X = ( 3+y).........( equ.3)
y/2 - 2(3+y) = 30
y/2 - 6 + 2y = 30
multiply both side by 2
y - 6 + 2y = 60
y + 2y = 60 - 6
3y = 54
Y = 18
from equ.3
X = 3+Y where y is 18
X = 3+18 = 21