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.