Simplify without using tables \(\frac{log_26}{log_28}\) - \(\frac{log_23}{2log_2\frac{1}{2}}\)

A.

\(\frac{1}{5}\)

B.

\(\frac{1}{2}\)

C.

\(\frac{-1}{2}\)

D.

(\frac{log_23}{log_27}\)

Correct answer is A

log\(_2\)6 - log\(_2\)3 = log\(_2\) (\(\frac{6}{3}\))

= log\(_2\)2... A

log\(_2\)8 - 2log\(_2\)\(\frac{1}{2}\)

log\(_2\)8 - log\(_2\)\(\frac{1}{2}\)\(^2\)

log\(_2\)8 - log\(_2\)\(\frac{1}{4}\)

= log\(_2\) 32... B

\(\frac{A}{B}\) = \(\frac{log_22}{log_232}\)

N.B. log\(_2\)2 = 1

= \(\frac{1}{5}\)