Question

What is the name of the rule that allows this to be true? And is it actually true?

If b/n = Log[a] then b = Log[a^n]

Answer 1

And I guess also, what is the principle here that allows it to be true?

Answer 2

Oh and does the base make any difference?
If b/n = Log_E[a] then b = Log_E[a^n]

Answer 3

Yep, that is true. It is the exponent rule.

Answer 4

It is true for the same reason that when you raise an exponent to another exponent, they multiply.

Answer 5

Got it, T/Y, So I could just quote 'the exponent rule' as an explanation for where this applies

Answer 6

I think the technical name is the logarithmic power rule.

Answer 7

yw :-)

Answer 8

Ah I see, so Log power rule...
if n=3
Log (a^n) = Log(a^3) = Log(a . a . a) = Log(a) + Log(a) + Log(a) = 3 Log(a)
and because
1 = 3 Log(a)
1/3 = 3 Log(a) /3
1/3 = Log(a)

Answer 9

Yep :-)