Question

Select the equation that has the same solution as the equation below. 5^(2x-5)= 125

Answer 1

The equation that has the same solution as $5^{(2x-5)} = 125$ is: C.$64 = 2^{(3x - 6)}$

How to Solve Equations having Exponents

• To solve such, simplify the bases so that the base on the right equals the base on the left.
• Then solve the equation for the variable.

Given:

$5^{(2x-5)} = 125\\\\5^{(2x-5)} = 5^3$

• The bases will cancel out

2x - 5 = 3

• Solve for x

2x = 3 + 5

2x = 8

x = 4

The solution of $5^{(2x-5)} = 125$ is 4.

Thus:

$64 = 2^{(3x - 6)}\\\\2^6 = 2^{(3x - 6)}\\\\6 = 3x - 6\\6 + 6 = 3x\\12 = 3x\\4 = x\\x = 4$

Therefore the equation that has the same solution as $5^{(2x-5)} = 125$ is: C.$64 = 2^{(3x - 6)}$

Learn more about equations with exponents on:

brainly.com/question/11832081