Questions: Rewrite each equation as requested. (a) Rewrite as an exponential equation. log8 1=0 (b) Rewrite as a logarithmic equation. 3^4=81 (a) = (b) log =

Transcript text: Rewrite each equation as requested. (a) Rewrite as an exponential equation. \[ \log _{8} 1=0 \] (b) Rewrite as a logarithmic equation. \[ 3^{4}=81 \] (a) $\square$ $=$ $\square$ (b) $\log _{\square} \square=$ $\square$

Solution

Solution Steps

Step 1: Rewrite the logarithmic equation as an exponential equation

The given logarithmic equation is: \[ \log _{8} 1=0 \] To rewrite this as an exponential equation, recall that $\log_b a = c$ is equivalent to $b^c = a$. Applying this to the given equation: \[ 8^0 = 1 \]

Step 2: Rewrite the exponential equation as a logarithmic equation

The given exponential equation is: \[ 3^{4}=81 \] To rewrite this as a logarithmic equation, recall that $b^c = a$ is equivalent to $\log_b a = c$. Applying this to the given equation: \[ \log _{3} 81=4 \]

Step 3: Fill in the blanks for part (a)

The equation $8^0 = 1$ corresponds to the blanks in part (a): \[ 8^0 = 1 \]

Step 4: Fill in the blanks for part (b)

The equation $\log _{3} 81=4$ corresponds to the blanks in part (b): \[ \log _{3} 81=4 \]