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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.

Respuesta :

amna04352

Answer:

lg21/(3lg2)

Step-by-step 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)

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

[tex]\log_a(b)=\dfrac{\ln(b)}{\ln(a)}[/tex]

So, you have

[tex]\log_8(21)=\dfrac{\ln(21)}{\ln(8)}[/tex]

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