A.22 B.68 C.118 D.119

I NEED HELP!! please show all work

PtichkaEL [24]

Take the logarithm of both sides. The base of the logarithm doesn't matter.

$4^{5x} = 3^{x-2}$

$\implies \log 4^{5x} = \log 3^{x-2}$

Drop the exponents:

$\implies 5x \log 4 = (x-2) \log 3$

Expand the right side:

$\implies 5x \log 4 = x \log 3 - 2 \log 3$

Move the terms containing x to the left side and factor out x :

$\implies 5x \log 4 - x \log 3 = - 2 \log 3$

$\implies x (5 \log 4 - \log 3) = - 2 \log 3$

Solve for x by dividing boths ides by 5 log(4) - log(3) :

$\implies \boxed{x = -\dfrac{ 2 \log 3 }{ 5 \log 4 - \log 3 }}$

You can stop there, or continue simplifying the solution by using properties of logarithms:

$\implies x = -\dfrac{ \log 3^2 }{ \log 4^5 - \log 3 }$

$\implies x = -\dfrac{ \log 9 }{ \log 1024 - \log 3 }$

$\implies \boxed{x = -\dfrac{ \log 9 }{ \log \frac{1024}3 }}$

You can condense the solution further using the change-of-base identity,

$\implies \boxed{x = -\log_{\frac{1024}3}9}$

5 0

2 years ago

9 is the geometric mean between 4 and which other number?

KonstantinChe [14]

Answer is A. 20.25

cause 20.25 x 9 = 81
√81 = 9
so 9 is the geometric mean between 4 and 20.25

5 0

3 years ago

In triangle ABC, the measure of ∠B is 90°, BC=16, and AC=20. Triangle DEF is similar to triangle ABC, where vertices D, E, and F

nevsk [136]

The third side of triangle ABC is AB. Using the Pythagorean Theorem, its length is 12.
12² + 16² = 20²

∠F is congruent to ∠C and so the sin(∠F) = sin(∠C)

The sin(∠C) = opposite/hypotenuse
= |AB| / |AC|
= 12/20
= 3/5
= 0.6

Answer:
Yes, it is 0.6

6 0

2 years ago

Pythagorean theorem

gulaghasi [49]

3 √10
I think since a^2+b^2=c^2

5 0

2 years ago

Read 2 more answers

Tom planted 1/2 of an 8-ft by 9-ft garden with vegetables. He planted tomatoes in 1/3 of the vegetable garden and corn in the re

ser-zykov [4K]

Answer:

Corn was planted in 24 sq.ft. of the vegetable garden.