Question

log1.2 bar base 3/4​

Answer 1

SOLUTION

TO DETERMINE

CORRECT QUESTION

$\displaystyle \sf{ log_{ \frac{3}{4} }(1. \bar{3}) }$

FORMULA TO BE IMPLEMENTED

We are aware of the formula on logarithm that

$\displaystyle \sf{1. \: \: log_{ a}( {b}^{m} ) = m log_{a}(b) }$

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

EVALUATION

$\displaystyle \sf{ log_{ \frac{3}{4} }(1. \bar{3}) }$

$= \displaystyle \sf{ log_{ \frac{3}{4} } \bigg( \frac{13 - 1}{9} \bigg) }$

$= \displaystyle \sf{ log_{ \frac{3}{4} } \bigg( \frac{12}{9} \bigg) }$

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

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

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

$= - 1 \times 1$

$= - 1$

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