Question

log9/log√3
step by step needed​

Answer 1

Answer:

1.576643741233

Step-by-step explanation:

Answer 2

Answer:

4

Step-by-step explanation:

Given :

$\mathrm{\dfrac{log9}{log\sqrt3}}$

To find :

The value of the given logarithm

Solution :

We know that,

$\boxed{\mathrm{loga^m = mloga}}$

So, here,

$\longmapsto \mathrm{\dfrac{log9}{log\sqrt3}}$

$\implies \mathrm{\dfrac{log9}{\dfrac{1}{2}log3}}$

$\implies \mathrm{\dfrac{2log9}{log3}}$

We know that,

$\boxed{\mathrm{\dfrac{loga}{logb} = log_ba}}$

$\implies \mathrm{2log_39}$

$\implies \mathrm{2log_33^2}$

$\implies \mathrm{4log_33}$

We know that,

$\boxed{\mathrm{log_aa = 1}}$

So,

$\implies \mathrm{4log_33 = 4 \times 1}$

$\implies \underline{\underline{4}}$

$\therefore \underline{\boxed{\mathbf{\dfrac{log9}{log\sqrt3}} = 4}}$

Hope it helps!!