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lisapressley2001
lisapressley2001 lisapressley2001
  • 05-01-2017
  • Mathematics
Answered

2.What is the solution of the solution of the equation 5^3x=15? Round to the nearest ten thousandth.

Verified Answer :

apologiabiology
apologiabiology apologiabiology
  • 05-01-2017

hmm
remember
\(a^c=b\) can translate to \(log_a(b)=c\)
so

\(5^{3x}=15\) can translate to \(log_5(15)=3x\)
divide both sides by 3
\((1/3)log_5(15)=x\)
\(log_5(15^{1/3})=x\)
use calculator, if you can't use change of base formula to do it
\(log_a(b)= \frac{log_c(b)}{log_c(a)}\) so
\(log_5(10^{1/3})= \frac{log_{10}(15^{1/3})}{log_{10}(5)}=x\)
evaluate using base 10 on your calculator
0.560869=x

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