Question

If logx (1/343) = 3, then the value of x is equal to

Answer 1

SOLUTION

GIVEN

$\displaystyle \sf{} log_{x} \bigg( \frac{1}{343} \bigg) = 3$

TO DETERMINE

The value of x

FORMULA TO BE IMPLEMENTED

$\displaystyle \sf{} 1. \: \: \: log_{x} a = m \: \: \: implies \: \: a = {x}^{m}$

$\sf{}2. \: \: {( {a}^{m} )}^{n} = {a}^{mn}$

EVALUATION

Here it is given that

$\displaystyle \sf{} log_{x} \bigg( \frac{1}{343} \bigg) = 3$

$\implies \displaystyle \sf{} {x}^{3} = \frac{1}{343}$

$\implies \displaystyle \sf{} {x}^{3} = {343}^{ - 1}$

$\implies \displaystyle \sf{} {x}^{3} = {( {7}^{3}) }^{ - 1}$

$\implies \displaystyle \sf{} {x}^{3} = {(7)}^{ - 3}$

$\implies \displaystyle \sf{} {x}^{3} = {( {7}^{ - 1}) }^{ 3}$

$\implies \displaystyle \sf{} x = {7}^{ - 1}$

$\implies \displaystyle \sf{} x = \frac{1}{7}$

FINAL ANSWER

$\displaystyle \sf{} The \: required \: value \: of \: \: x \: is \: \: \frac{1}{7}$

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