Question

Write in Logarithmic Form:
125 = 5 ^ 3

A. Log (base 125) 5 = 3
B. Log (base 3) 125 = 5
C. Log (base 5) 125 = 3

Answer 1

Task. Write in Logarithmic Form: $125 = 5^3$.

A. $\log_{125} 5 = 3$

B. $\log_3 125 = 5$

C. $\log_5 125 = 3$

Solution. Recall that for $a.b.c > 0$ and $b \neq 1$ the relation

$$\log_a b = c$$

is equivalent to

$$b = a^c.$$

We have that

$$125 = 5^3,$$

so $a = 5$, $b = 125$ and $c = 3$. Hence the latter identity is equivalent to $\log_a b = c$, i.e.

$$\log_5 125 = 3.$$

Thus the correct answer is C.