Question

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

PS: the first log is log base 5 of x and the second log is log base 5 of 4

Answer 1

x = ±2

Explanation:

A equation is given to us , which is ,

`\longrightarrow 2log_5(x) = log_5 4`

From properties of logarithm we know that ,

`\longrightarrow alog\ m = log \ m^a`

Applying this to LHS , we have ;

`\longrightarrow log_5 x^2 = log_5 4`

Now the bases of logarithm on LHS and RHS is same . On comparing , we have ;

`\longrightarrow x^2 = 4`

Put square root on both sides,

`\longrightarrow x =√(4)`

Simplify ,

`\longrightarrow \underline{\underline{ x =\pm 2 }}`

This is the required answer.