Question

Evaluate the logarithm. *logs 729​

Answer 1

Answer:

$\log _{10}\left(s\right)+6\log _{10}\left(3\right)$

(Please vote me Brainliest if this helped!)

Step-by-step explanation:

$\log _{10}\left(s\cdot \:729\right)$

$\mathrm{Apply\:log\:rule}:\quad \log _c\left(ab\right)=\log _c\left(a\right)+\log _c\left(b\right)$

$\log _{10}\left(s\cdot \:729\right)=\log _{10}\left(s\right)+\log _{10}\left(729\right)$

$=\log _{10}\left(s\right)+\log _{10}\left(729\right)$

$\log _{10}\left(729\right)$

$\mathrm{Rewrite\:}729\mathrm{\:in\:power-base\:form:}\quad 729=3^6$

$=\log _{10}\left(3^6\right)$

$\mathrm{Apply\:log\:rule}:\quad \log _a\left(x^b\right)=b\cdot \log _a\left(x\right)$

$\log _{10}\left(3^6\right)=6\log _{10}\left(3\right)$

$=6\log _{10}\left(3\right)$

$=\log _{10}\left(s\right)+6\log _{10}\left(3\right)$