The equation that has the same solution as [tex]5^{(2x-5)} = 125[/tex] is: C.[tex]64 = 2^{(3x - 6)}[/tex]
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:
[tex]5^{(2x-5)} = 125\\\\5^{(2x-5)} = 5^3\\[/tex]
- The bases will cancel out
2x - 5 = 3
2x = 3 + 5
2x = 8
x = 4
The solution of [tex]5^{(2x-5)} = 125[/tex] is 4.
Thus:
[tex]64 = 2^{(3x - 6)}\\\\2^6 = 2^{(3x - 6)}\\\\6 = 3x - 6\\6 + 6 = 3x\\12 = 3x\\4 = x\\x = 4[/tex]
Therefore the equation that has the same solution as [tex]5^{(2x-5)} = 125[/tex] is: C.[tex]64 = 2^{(3x - 6)}[/tex]
Learn more about equations with exponents on:
https://brainly.com/question/11832081
