# Solve the equation #25log_2x=log_x2# ?

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#25log_2x=log_x2#

I have gotten to #logx^25=1/(logx)# but I am not sure how to proceed from here. I am supposed to solve this without the use of a calculator, and the answer is given as #x=2^((+/-)1/5)# . How should I go about solving this?

I have gotten to

##### 2 Answers

I tried this:

#### Explanation:

I would try changing the base of the second log as:

so we get:

rearrange:

take the square root of both sides to get rid of the square:

apply the definition of log:

#### Explanation: