Evelyn Freeman

2022-10-20

Which expression is equivalent to ${\mathrm{log}}_{7}\left(2a+8b\right)$

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cokeman206

Expert

$lo{g}_{7}\left(2a+8b\right)\phantom{\rule{0ex}{0ex}}={\mathrm{log}}_{7}2\left(a+4b\right)\phantom{\rule{0ex}{0ex}}={\mathrm{log}}_{7}2+{\mathrm{log}}_{7}\left(a+4b\right)\phantom{\rule{0ex}{0ex}}\left[\because \mathrm{log}\left(xy\right)=\mathrm{log}x+\mathrm{log}y\right]$
$\therefore$ The expression ${\mathrm{log}}_{7}2+{\mathrm{log}}_{7}\left(a+4b\right)$
is equivalent to ${\mathrm{log}}_{7}\left(2a+8b\right)$

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