Question

If log1227 = a then log316 in terms of a is _______.

Answer 1

please mark me brain mark list

Answer 2

SOLUTION

GIVEN

$\displaystyle \sf{ log_{12}(27) = a }$

TO DETERMINE

$\displaystyle \sf{ log_{3}(16) }$

EVALUATION

$\displaystyle \sf{ log_{12}(27) = a }$

$\displaystyle \sf{ \implies \: \frac{ log(27) }{ log(12) } = a }$

$\displaystyle \sf{ \implies \: \frac{ log( {3}^{3} ) }{ log( {2}^{2} \times 3 ) } = a }$

$\displaystyle \sf{ \implies \: \frac{3 log( 3 ) }{ 2log 2 + log 3 } = a }$

$\displaystyle \sf{ \implies \: \frac{ log( 3 ) }{ 2log 2 + log 3 } = \frac{a}{3} }$

$\displaystyle \sf{ \implies \: \frac{ 2log 2 + log( 3 ) }{ log 3 } = \frac{3}{a} }$

$\displaystyle \sf{ \implies \: \frac{ 2log 2 }{ log 3 } + 1 = \frac{3}{a} }$

$\displaystyle \sf{ \implies \: \frac{ 2log 2 }{ log 3 } = \frac{3}{a} - 1}$

$\displaystyle \sf{ \implies \: \frac{ 2log 2 }{ log 3 } = \frac{3 - a}{a} }$

$\displaystyle \sf{ \implies \: \frac{ log 2 }{ log 3 } = \frac{3 - a}{2a} }$

$\displaystyle \sf{ \implies \: \frac{4 log 2 }{ log 3 } = \frac{4(3 - a)}{2a} }$

$\displaystyle \sf{ \implies \: \frac{ log {2}^{4} }{ log 3 } = \frac{2(3 - a)}{a} }$

$\displaystyle \sf{ \implies \: \frac{ log 16 }{ log 3 } = \frac{2(3 - a)}{a} }$

$\displaystyle \sf{ \implies \: log_{3}(16) = \frac{2(3 - a)}{a} }$

FINAL ANSWER

$\displaystyle \sf{ \: log_{3}(16) = \frac{2(3 - a)}{a} }$

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

1. If log (0.0007392)=-3.1313 , then find log(73.92)

https://brainly.in/question/21121422

2.If 2log((x+y)/(4))=log x+log y then find the value of (x)/(y)+(y)/(x)

https://brainly.in/question/24081206