Question

explain step by step by step
(logx2)^2 - (log2x)^2=log`2x(2/x)is

Answer 1

\[(\log _{x}2)^2 (\log _{2}x)^2 = \log _{2x}(2/x) is\]

Answer 2

pls help

Answer 3

Is it a minus or are they multiplying?

Answer 4

Okay we need to write the logs to the base 2x.

\[log_x 2=\frac{log_{2x} 2}{log_{2x} x}\]\[log_2 x=\frac{log_{2x} x}{log_{2x} 2}\]

Answer 5

so the answer will br \[1/\sqrt{2}\]

Answer 6

\[(log_x 2)^2 -(log_2 x)^2=(\frac{log_{2x} 2}{log_{2x} x})^2-(\frac{log_{2x} x}{log_{2x} 2})^2\]\[=log_{2x} (\frac{2}{x})^2-log_{2x} (\frac{x}{2})^2\]\[=log_{2x} (\frac{4}{x^2})^2\]
So \[log_{2x} \frac{16}{x^4}=log_{2x} \frac{2}{x}\]\[16/x^4=2/x\]\[8=x^3\]\[x=2\]

Answer 7

How did you get your answer?

Answer 8

Zed i dont agree to u!! its unsatisfactory!