Question 566887
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 1.51^x\ =\ 70]


Take the log of both sides -- any base, it doesn't matter.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ln\left(1.51^x\right)\ =\ \ln(70)]


Use


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \log_b(x^n)\ =\ n\log_b(x)]


to write:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ln\left(1.51\right)\ =\ \ln(70)]


Then


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ \frac{\ln(70)}{\ln\left(1.51\right)}]


The rest is calculator work.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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