Alg9.4.11

Find the value of $\log_\sqrt7(343)\,$

Expressing the log number in terms of the base,we get

$\log_\sqrt{7}(7^3)\,$

As per the formula $\log_a(a^m)=m\log_a(a)\,$

$3\log_\sqrt{7}(7)\,$

And applying another formula $\log_a^{n}(a^m)=\frac{m}{n}\,$

we get

$3\cdot\frac{1}{\frac{1}{2}}\,$

which is equal to

$3\cdot2\,$

Hence the value is

$\log_\sqrt7(343)=6\,$