Question

log of x with base 5 +1 = 2 log of 5 with base x​

Answer 1

$log_{5}x+1=2*log_{x}5$

We know that  $log_{b}a=\frac{1}{log_{a}b}$

Let $log_{5}x$ = k

k + 1 =  $\frac{2}{k}$

$k^2+k=2$

$k^2+k-2=0\\k^2+2k-k-2=0\\k(k+2)-1(k+2)=0\\(k-1)(k+2)=0$

k = 1 or (-2)

$log_{5}x$ = 1 or (-2)

x = 5 or $\frac{1}{25}$