How do you simplify \log_{5} ( b^{2} a^{8} )?

Oct 7, 2016

Explanation:

Because of logarithmic rules, which can be seen on this page http://mathsvideos.net/log-formulas/, what you see below is true.

${\log}_{5} \left({b}^{2} {a}^{8}\right)$

$= {\log}_{5} \left({\left(b {a}^{4}\right)}^{2}\right)$

$= 2 {\log}_{5} \left(b {a}^{4}\right)$

$= 2 \left\{{\log}_{5} \left(b\right) + {\log}_{5} \left({a}^{4}\right)\right\}$

$= 2 \left\{{\log}_{5} \left(b\right) + 4 {\log}_{5} \left(a\right)\right\}$

$= 2 {\log}_{5} \left(b\right) + 8 {\log}_{5} \left(a\right)$

You can find out why the above transformations are mathematically coherent by accessing this playlist: https://www.youtube.com/playlist?list=PLFM03zQeSz2PvB2IxWqcLcZMSIIpcIVtV