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

Select The Equation That Has The Same Solution As The Equation Below 52x5 125 class=

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Akposevictoridn

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

  • Solve for x

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

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