Simplify without using tables \(\frac{log_26}{log_28}\) - \(\frac{log_23}{log_2\frac{1}{2}}\)
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Correct Answer: Option A
Explanation:
log26 - log23 = log2 (\(\frac{6}{3}\)) = log22
log28 - 2\(\frac{1}{2}\) log28 - log2\(\frac{1}{2}\) log28 - log2\(\frac{1}{4}\)
\(\frac{log_22}{log_232} = \frac{log_22}{5log_22}\)
= \(\frac{1}{5}\)
N.B. log22 = 1
log26 - log23 = log2 (\(\frac{6}{3}\)) = log22
log28 - 2\(\frac{1}{2}\) log28 - log2\(\frac{1}{2}\) log28 - log2\(\frac{1}{4}\)
\(\frac{log_22}{log_232} = \frac{log_22}{5log_22}\)
= \(\frac{1}{5}\)
N.B. log22 = 1