Write the equation in its equivalent exponential form.
$\log _{b} 216=3$
(A) $216^{b}=3$
(B) $216^{3}=b$
$b^{3}=216$
D) $3^{b}=216$

Answer

Expert–verified

Hide Steps

Answer

$\boxed{b^{3}=216}$

Steps

Step 1 ：Write the equation in its equivalent exponential form: $\log _{b} 216=3$

Step 2 ：Use the formula $\log_{b}a = c$ is equivalent to $b^c = a$, where $b$ is the base, $216$ is the value of $a$, and $3$ is the value of $c$

Step 3 ：Calculate the base: $b^3 = 216$

Step 4 ：$\boxed{b^{3}=216}$