Asked by Tiger Ale
How do you use the law of logarithms to calculate for u^c=(a^r)^c?
Answers
Answered by
oobleck
not sure what you want to do, but taking logs,
log(u^c) = c logu
(a^r)^c = a^(rc)
so log((a^r)^c) = rc loga
c logu = rc loga
logu = r loga
r = log<sub><sub>a</sub></sub>u
but even without logs, if a^c = b^c, then a=b
so, u = a^r
log(u^c) = c logu
(a^r)^c = a^(rc)
so log((a^r)^c) = rc loga
c logu = rc loga
logu = r loga
r = log<sub><sub>a</sub></sub>u
but even without logs, if a^c = b^c, then a=b
so, u = a^r
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