Question

find the value of log 4/3 to the base 3/4

Answer 1

SOLUTION

TO DETERMINE

The value of

$\displaystyle \sf{ log_{ \frac{3}{4} } \bigg( \frac{4}{3} \bigg) }$

FORMULA TO BE IMPLEMENTED

$\displaystyle \sf{ 1. \: \: log( {x}^{n} ) = n log(x) }$

$\displaystyle \sf{2. \: \: log_{x}(x) = 1}$

EVALUATION

$\displaystyle \sf{ log_{ \frac{3}{4} } \bigg( \frac{4}{3} \bigg) }$

$\displaystyle \sf{ = log_{ \frac{3}{4} } {\bigg( \frac{3}{4} \bigg)}^{ - 1} }$

$\displaystyle \sf{ = - 1 \times log_{ \frac{3}{4} } {\bigg( \frac{3}{4} \bigg)}^{ } \: \: \: (by \: formula \: 1)}$

$\displaystyle \sf{ = - 1 \times 1 \: \: \: (by \: formula \: 2)}$

$\displaystyle \sf{ = - 1}$

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