Question

convert each logarithmic equation into its equivalent exponential form.
a) \\(\log_{4}(64) = 3\\)
exponential equation
b) \\(\log_{2}(32) = 5\\)
exponential equation
c) \\(\log_{3}(9) = 2\\)
exponential equation

Explanation:

Part a)

Step1: Recall log to exp rule

The logarithmic form $\log_b(a) = c$ converts to exponential form $b^c = a$.

Step2: Apply to $\log_4(64) = 3$

Here, $b = 4$, $c = 3$, $a = 64$. So exponential form is $4^3 = 64$.

Step1: Recall log to exp rule

Use $\log_b(a) = c \implies b^c = a$.

Step2: Apply to $\log_2(32) = 5$

Here, $b = 2$, $c = 5$, $a = 32$. So exponential form is $2^5 = 32$.

Step1: Recall log to exp rule

Use $\log_b(a) = c \implies b^c = a$.

Step2: Apply to $\log_3(9) = 2$

Here, $b = 3$, $c = 2$, $a = 9$. So exponential form is $3^2 = 9$.

Answer:

$4^3 = 64$

Part b)