Question

Evaluate the following expression log3 9

Answer 1

Answer: The solution for the given expression is 2.

Step-by-step explanation:

We are given:

An expression having value:  $\log_3 9$

Using the identities:

$\log_a x^n=n\log_a x$       ......(1)

$\log_a a=1$        ......(2)

Evaluating the expression:

$\Rightarrow \log_3 9=\log _3 3^2$

Using identity 1:

$\Rightarrow \log _3 3^2=2\log_3 3$

Using identity 2:

$2\log_3 3=2\times 1=2$

Hence, the solution for the given expression is 2.

Answer 2

$\bf \textit{Logarithm Cancellation Rules} \\\\ \boxed{log_a a^x = x}\qquad \qquad a^{log_a x}=x\\\\ -------------------------------\\\\ log_3(9)\qquad \qquad \underline{9=3^2}\qquad \qquad log_3(\underline{3^2})\implies 2$