Respuesta :

[tex]\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[/tex]

Answer: The solution for the given expression is 2.

Step-by-step explanation:

We are given:

An expression having value:  [tex]\log_3 9[/tex]

Using the identities:

[tex]\log_a x^n=n\log_a x[/tex]       ......(1)

[tex]\log_a a=1[/tex]        ......(2)

Evaluating the expression:

[tex]\Rightarrow \log_3 9=\log _3 3^2[/tex]

Using identity 1:

[tex]\Rightarrow \log _3 3^2=2\log_3 3[/tex]

Using identity 2:

[tex]2\log_3 3=2\times 1=2[/tex]

Hence, the solution for the given expression is 2.

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