Question

What is log(z^4/5) written in expanded form?

Answer 1

To get answer:

$\mathrm{Apply\:log\:rule}:\quad \log _c\left(\frac{a}{b}\right)=\log _c\left(a\right)-\log _c\left(b\right)\\\log _{10}\left(\frac{z^4}{5}\right)=\log _{10}\left(z^4\right)-\log _{10}\left(5\right)\\=\log _{10}\left(z^4\right)-\log _{10}\left(5\right)\\\mathrm{Simplify}\:\log _{10}\left(z^4\right)\\\log _{10}\left(z^4\right)\\\mathrm{Apply\:log\:rule\:}\log _a\left(x^b\right)=b\cdot \log _a\left(x\right),\:\quad \mathrm{\:assuming\:}x\:\ge \:0\\=4\log _{10}\left(z\right)$

Answer: $4\log _{10}\left(z\right)-\log _{10}\left(5\right)$

Answer: 4logz−log5