Question

what is the value of log9 27+log8 32

Answer 1

for solution refer attachment

Answer 2

Hey there!

If x^n = a then the logarithmic form of it is $log_{x}(a) = n$ where a, x are positive integers and a ≠ 1

Logarithms follow some rules that,

logm^n = nlogm

logm + logn = logmn

Now given,

$log_{9}(27) + log_{8}(32) \\ \\ => log_{3^2}(3^3) + log_{2^3}(2^5) \\ \\ => \frac{3}{2} log_{3}(3) + \frac{5}{2} log_{2}{2} \\ \\ => \frac{3}{2} + \frac{5}{3} \\ \\ => \frac{9+10}{6} \\ \\ => \frac{19}{6}$

I used the concept of
1) $log_{a}(m^{n})= n log_{a}(m)$
2 ) $log_{a^n}(m) = \frac{1}{n} log_{a}(m)$

Hope you are helped