Answer with step-by-step explanation:
We are given three different expressions and we are to write an equivalent exponential equation for them.
We know that the standard form of a logarithmic expression is given by:
[tex]y = log_a ( x )[/tex] which is equivalent to the exponential form [tex]x = a ^ y[/tex].
1. [tex] log _ {10} (0.1) = -1 [/tex] ---> [tex]10^{-1}=0.1[/tex]
2. [tex] log _ {3} 9 = 2 [/tex] ---> [tex]3^2=9[/tex]
3. [tex] log _ 5 ( \frac { 1 } { \sqrt { 5 } } ) = -\frac { 1 } { 2 } [/tex] ---> [tex]5^{-\frac{1}{2} }=\frac{1}{\sqrt{5} }[/tex]
