Solve the exponential equation 125^x = 625 by expressing each side as a po

facas9

facas9

Answered question

2021-09-19

Solve the exponential equation 125x=625 by expressing each side as a power of the same base and then equating exponents.

Answer & Explanation

Leonard Stokes

Leonard Stokes

Skilled2021-09-20Added 98 answers

Given that:
The exponential equation 125x=625
To use:
Exponential equation with same base.
ax=by if and only x=y
First to rewrite the given exponential equation as the power of the same base.
Let 125x=625
Also,
125=5×5×5
=53
and
625=5×5×5×5
=54
To get,
125=53 and 625=54
Then,
125x=625
(53)x=54
53x=54
To use the exponential equation with the same base.
To get,
3x=4
To solve for x,
Dividing on both side by 3,
To get,
x=43

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