Question

Rewrite as a quotient of two common logarithms. Write your answer in simplest form.

log base of 8 (21)

idk if you can figour out what that is but please help.

Answer 1

lg21/(3lg2)

Explanation:

log8(21)

Common log: log10 or lg

logb(a)

Change of base law:

logc(a)/logc(b)

log8(21)

lg21/lg8

8 = 2³

log8 = lg2³ = 3lg2

lg21/(3lg2)

Answer 2

By "common logarithm" you probably mean the natural logarithm. And you'll need the formula to change base:

`\log_a(b)=(\ln(b))/(\ln(a))`

So, you have

`\log_8(21)=(\ln(21))/(\ln(8))`