Question

rewrite each equation as requested.
(a) rewrite as a logarithmic equation.
$5^2 = 25$
$log_{\square}\square = \square$
(b) rewrite as an exponential equation.
$log_{2} \frac{1}{16} = -4$
$\square^{\square} = \square$

Explanation:

Step1: Recall the logarithmic definition

The exponential form \(a^b = c\) can be rewritten as the logarithmic form \(\log_a c = b\).

Step2: Rewrite \(5^2 = 25\) as logarithmic equation

For \(5^2 = 25\), using the definition \(a = 5\), \(b = 2\), \(c = 25\), so \(\log_{5} 25 = 2\).

Step3: Recall the exponential form from logarithmic form

The logarithmic form \(\log_a c = b\) can be rewritten as the exponential form \(a^b = c\).

Step4: Rewrite \(\log_{2} \frac{1}{16} = -4\) as exponential equation

For \(\log_{2} \frac{1}{16} = -4\), using the definition \(a = 2\), \(b = -4\), \(c = \frac{1}{16}\), so \(2^{-4} = \frac{1}{16}\).

Answer:

(a) \(\log_{5} 25 = 2\) (so the blanks are 5, 25, 2 respectively)
(b) \(2^{-4} = \frac{1}{16}\) (so the blanks are 2, -4, \(\frac{1}{16}\) respectively)