Question

solve 9 log 2 to the base 3​

Answer 1

log base 9 of x + log base 3 of x=6

logx/log 9 +log x/log 3=6

log x/ 2log3 +log x/log 3=6

(log x/ log 3 ).(1/2+1)=6

log x/log3 =6×2/3=4

log x= 4.log 3

log x= log (3)^4

log x= log 81

x=81 , answer.

Answer 2

$\displaystyle \sf{ {9}^{ log_{3}(2) } } = \bf 4$

Correct question :

$\displaystyle \sf{ Solve :\: \: {9}^{ log_{3}(2) } }$

Given :

$\displaystyle \sf{ {9}^{ log_{3}(2) } }$

To find :

The value of the expression

Solution :

Step 1 of 2 :

Write down the given expression

Here the given expression is

$\displaystyle \sf{ {9}^{ log_{3}(2) } }$

Step 2 of 2 :

Simplify the given expression

$\displaystyle \sf{ Let\: \: x = {9}^{ log_{3}(2) } }$

Taking logarithm in both sides we get

$\displaystyle \sf{ log \: x = log \: \bigg( {9}^{ log_{3}(2) } \bigg) }$

$\displaystyle \sf{ \implies }log \: x = log \: 9 \times log_{3}(2)$

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

$\displaystyle \sf{ \implies }log \: x = 2log \: {3}^{} \times \frac{log \: 2}{log \: 3}$

$\displaystyle \sf{ \implies }log \: x = 2log \: {2}^{}$

$\displaystyle \sf{ \implies }log \: x = log \: {2}^{2}$

$\displaystyle \sf{ \implies }log \: x = log \: 4$

$\displaystyle \sf{ \implies }x = 4$

$\boxed{ \: \: \displaystyle \sf{ \therefore \: {9}^{ log_{3}(2) } } = 4\: \: }$

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