Question

Log base 3 root 2 of 324

Answer 1

factor of 324
will be
2*2*3*3*3*3
which is clearly equals to
${3 \sqrt{2} }^{4}$
hence ans is 4

Answer 2

The value of$\log_{(3\sqrt{2})}324$ is "4".

Step-by-step explanation:

Let x =$\log_{(3\sqrt{2})}324$    ..... (1)

To find, the value of $\log_{(3\sqrt{2})}324$= ?

∴ 324 = 2 × 2 × 3 × 3 × 3 × 3

$=2^{2} \times 3^{4}$

$=\sqrt{2}^{4} \times 3^{4}$

$=(3\sqrt{2})^{4}$

Now, equation (1) becomes

$x = \log_{(3\sqrt{2})}(3\sqrt{2})^{4}$

$x =4 \log_{(3\sqrt{2})}(3\sqrt{2})$

= 4

[ ∵ $\log_aa$ = 1 ]

Hence, the value of$\log_{(3\sqrt{2})}324$ is "4".