Welcome to Westonci.ca, where curiosity meets expertise. Ask any question and receive fast, accurate answers from our knowledgeable community. Discover comprehensive solutions to your questions from a wide network of experts on our user-friendly platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

Rewrite each equation as requested:

(a) Rewrite as an exponential equation:
[tex]\[ \log_3 81 = 4 \][/tex]

(b) Rewrite as a logarithmic equation:
[tex]\[ 8^{-1} = \frac{1}{8} \][/tex]

(a) [tex]\(\square = \square\)[/tex]

(b) [tex]\(\log \square \square = \square\)[/tex]

Sagot :

Sure, let's rewrite each given equation step-by-step as requested.

### (a) Rewrite as an exponential equation.
The given logarithmic equation is:
[tex]\[ \log_3(81) = 4 \][/tex]

To rewrite it as an exponential equation, recall that [tex]\(\log_b(a) = c\)[/tex] means [tex]\(b^c = a\)[/tex]. Here, [tex]\(b = 3\)[/tex], [tex]\(a = 81\)[/tex], and [tex]\(c = 4\)[/tex]. Therefore:
[tex]\[ 3^4 = 81 \][/tex]

So, the exponential equation is:
[tex]\[ 3^4 = 81 \][/tex]

### (b) Rewrite as a logarithmic equation.
The given exponential equation is:
[tex]\[ 8^{-1} = \frac{1}{8} \][/tex]

To rewrite it as a logarithmic equation, recall that if [tex]\(b^c = a\)[/tex], then [tex]\(\log_b(a) = c\)[/tex]. Here, [tex]\(b = 8\)[/tex], [tex]\(a = \frac{1}{8}\)[/tex], and [tex]\(c = -1\)[/tex]. Therefore:
[tex]\[ \log_8 \left( \frac{1}{8} \right) = -1 \][/tex]

So, the logarithmic equation is:
[tex]\[ \log_8\left( \frac{1}{8} \right) = -1 \][/tex]

Putting it all together:

(a) [tex]\( 3^4 = 81 \)[/tex]

(b) [tex]\(\log_8 \left( \frac{1}{8} \right) = -1\)[/tex]