Question

If log(x-13)+3log2=log(3x+1) then find the value of x/3.

Answer 1

SOLUTION

GIVEN

$\sf{ \log(x - 13) \: + 3 \log 2= \log(3x + 1) \: }$

TO DETERMINE

$\sf{The \: value \: of \: \: \displaystyle \sf{ \frac{x}{3} \: }}$

EVALUATION

$\sf{ \log(x - 13) \: + 3 \log 2= \log(3x + 1) \: }$

$\implies \sf{ \log(x - 13) \: + \log {2}^{3} = \log(3x + 1) \: }$

$\implies \sf{ \log(x - 13) \: + \log 8 = \log(3x + 1) \: }$

$\implies \sf{ \log8(x - 13) \: = \log(3x + 1) \: }$

$\implies \sf{ 8(x - 13) \: = (3x + 1) \: }$

$\implies \sf{ 8x - 104\: = 3x + 1\: }$

$\implies \sf{ 5x = 105\: }$

$\implies \sf{ x = 21\: }$

Hence

$\sf{\displaystyle \sf{ \frac{x}{3} \: }}$

$= \sf{\displaystyle \sf{ \frac{21}{3} \: }}$

$= \sf{\displaystyle \sf{7 }}$

RESULT

Hence the required answer is

$\sf{ \boxed{ \: \: \displaystyle \sf{ \frac{x}{3} = 7\: \: \: }}}$

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