HW help: Logs

[EightySix Four]

Can anyone help me come up with a reasonable explanation (mathematically of course) as to why the change of base formula for logarithms works?

Thanks in advance

 

[chuckywang]

Let x = log a (b) / log a (c)

Then x*log a (c) = log a (b)

log a (c^x) = log a (b)

c^x = b

x = log c (b)