Question

lesson: 4.5 (period a)
convert each logarithmic expression to an exponential expression
a) \\(\log_{5} 4 = 625\\)
b) \\(\log_{3} 243 = 5\\)

Explanation:

Step1: Recall log to exponent rule

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

Step2: Apply rule to part (a)

For $\log_5 625 = 4$, substitute $b=5$, $a=625$, $c=4$:
$5^4 = 625$

Step3: Apply rule to part (b)

For $\log_3 243 = 5$, substitute $b=3$, $a=243$, $c=5$:
$3^5 = 243$

Answer:

a) $5^4 = 625$
b) $3^5 = 243$