Question

Find the value of $lo{g}_{7}343$.

Answer 1

Let factorise 343. we get

So,$343=7\times 7\times 7$

$343=7^3$

So, $lo{g}_{7}343=lo{g}_7{7}^3$

now, as we know, $lo{g}_a{b}^n=nlog{a}^b$

& If $lo{g}_a^a$ is given, then

$lo{g}_a^a=1$

So, $lo{g}_{7}343=lo{g}_7{7}^3=3lo{g}_{7}7$

therefore, $lo{g}_{7}343=3$