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Simplify without using tables \(\frac{Log_26 - Log_23}{Log_28 - 2Log_2\frac{1}{2}}\)

Mathematics
JAMB 1987

Simplify without using tables \(\frac{Log_26 - Log_23}{Log_28 - 2Log_2\frac{1}{2}}\)

  • A. \(\frac{1}{5}\)
  • B. \(\frac{1}{2}\)
  • C. \(\frac{-1}{2}\)
  • D. \(\frac{log_23}{log_27}\)
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Correct Answer: Option A
Explanation

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

= \(\frac{1}{5}\)
 


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