Answer :
Answer:
[tex]\log _{10}\left(s\right)+6\log _{10}\left(3\right)[/tex]
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Step-by-step explanation:
[tex]\log _{10}\left(s\cdot \:729\right)[/tex]
[tex]\mathrm{Apply\:log\:rule}:\quad \log _c\left(ab\right)=\log _c\left(a\right)+\log _c\left(b\right)[/tex]
[tex]\log _{10}\left(s\cdot \:729\right)=\log _{10}\left(s\right)+\log _{10}\left(729\right)[/tex]
[tex]=\log _{10}\left(s\right)+\log _{10}\left(729\right)[/tex]
[tex]\log _{10}\left(729\right)[/tex]
[tex]\mathrm{Rewrite\:}729\mathrm{\:in\:power-base\:form:}\quad 729=3^6[/tex]
[tex]=\log _{10}\left(3^6\right)[/tex]
[tex]\mathrm{Apply\:log\:rule}:\quad \log _a\left(x^b\right)=b\cdot \log _a\left(x\right)[/tex]
[tex]\log _{10}\left(3^6\right)=6\log _{10}\left(3\right)[/tex]
[tex]=6\log _{10}\left(3\right)[/tex]
[tex]=\log _{10}\left(s\right)+6\log _{10}\left(3\right)[/tex]