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Question Number 33157 by Rio Mike last updated on 11/Apr/18

find k if  kloga= loga + log a^2 + log a^(3 ) + log a^4

$${find}\:{k}\:{if} \\ $$$${kloga}=\:{loga}\:+\:{log}\:{a}^{\mathrm{2}} +\:{log}\:{a}^{\mathrm{3}\:} +\:{log}\:{a}^{\mathrm{4}} \\ $$

Commented by Joel578 last updated on 11/Apr/18

log a^m  = m . log a    k log a = log a + 2 log a + 3 log a + 4 log a                  = 10 log a  k = 10

$$\mathrm{log}\:{a}^{{m}} \:=\:{m}\:.\:\mathrm{log}\:{a} \\ $$$$ \\ $$$${k}\:\mathrm{log}\:{a}\:=\:\mathrm{log}\:{a}\:+\:\mathrm{2}\:\mathrm{log}\:{a}\:+\:\mathrm{3}\:\mathrm{log}\:{a}\:+\:\mathrm{4}\:\mathrm{log}\:{a} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\mathrm{10}\:\mathrm{log}\:{a} \\ $$$${k}\:=\:\mathrm{10} \\ $$

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