Question

find the value of log base root 3 243​

Answer 1

The value of $\log _{\sqrt{3}} 243=10.$

Step-by-step explanation:

We have,

$\log _{\sqrt{3}} 243$

To find, the value of$\log _{\sqrt{3}} 243$=?

∴ $\log _{\sqrt{3}} 243$

$=\log _{\sqrt{3}} 3^5$

[ ∵ 243 = 3 × 3 × 3 × 3 × 3]

$=\log _{\sqrt{3}} (\sqrt{3}\times \sqrt{3})^5$

$=\log _{\sqrt{3}}(\sqrt{3}^2)^5$

$=\log _{\sqrt{3}}\sqrt{3}}^{2\times 5}$

[ ∵ $a^{m} \times a^{n} =a^{m+n}$]

$=\log _{\sqrt{3}}\sqrt{3}}^{10}$

$=10\log _{\sqrt{3}}\sqrt{3}}$

[ ∵ $\log a^m=m\log a$]

$=10\times 1$

[ ∵$\log_aa=1$]

= 10

Hence, the value of $\log _{\sqrt{3}} 243=10.$