Convert Between Logarithmic and Exponential Practice

1. Rewrite the following equation in logarithmic form.

   $\quad 0.25=2^{ \Large{-2}}$

   Rewrite the following equation in exponential form.

   $\quad \log_{8}{\left(512\right)}=3$

2. The $3$ points plotted below are on the graph of $y=b^x$.

   Based only on these $3$ points, plot the $3$ corresponding points that must be on the graph of $y=\log_b{x}$.

   
   

3. Table I contains outputs of the function $f(x)=b^x$ for some $x$ values, and Table II contains outputs of the function $g(x)=\log_b(x)$ for some $x$ values. In both functions, $b$ is the same positive constant.

   Fill in the missing values in the tables. If necessary, round your answer to three decimal places.

   You do not need a calculator.

   Table I

   
   

   $x$	$0.631$	_____	$2$	$2.183$
   $f(x)=b^x$	$2$	$6$	$9$	$11$

   
   

   Table II

   $x$	$2$	$3$	$6$	_____
   $g(x)=\log_{b}(x)$	$0.631$	$1$	$1.631$	$2$

   
   

4. Rewrite the following equation in logarithmic form.

   $\quad 25=5^{ \Large{2}}$

   Rewrite the following equation in exponential form.

   $\quad \log_{32}{\left(16\right)}=\dfrac{4}{5}$
   

Source: Khan Academy, https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:log-intro/e/understanding-logs-as-inverse-exponentials
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