Question

Select all of the potential solution(s) of the equation 2log5x=log54.

Answer 1

X= -2 and x= 2 are the answers

Answer 2

Given :$2log_{5} x^{2} =log_{5} 2^{2}$

To solve for x we use the logarithm rule for powers.

The log rule for powers states:

$mlog_{a}n =log_{a} n^{m}$

We apply this rule to the left side of the equation.

[tex] log_{5} x^{2} =log_{5} 4

Both sides have log with same base so it can be eliminated.

Eliminating log from both sides we have:

[tex] x^{2} =4

To solve for x we take root of both sides

x=2,-2.