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
                                                    There are no AI answers yet. The ability to request AI answers is coming soon!
                                            
                Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.