Question

3^x=1/9

Answer 1

x=-2

Answer 2

Hint :-
9=3^2
\(3^x=\dfrac{1}{3^2}\)

Answer 3

and remember this rule
\(\Huge \dfrac{1}{b^a}=b^{-a}\)

Answer 4

\[3^x=1/9\]
take the logarithm to base three on both sides
\[x=\log_3(1/9)\]

now express 1/9 as 3^n

and apply some log laws

\[\boxed{\log_b(z^n)=n\log_b(z)}\]\[\boxed{\log_b(b)=1}\]