53-log-x-7-x-x-

Question Number 76034 by hmamarques1994@gmail.com last updated on 22/Dec/19

53^{\log_{x} (7)} = \sqrt{x}

x = ?

Answered by MJS last updated on 22/Dec/19

53^{\frac{\ln 7}{\ln x}} = \sqrt{x}

\frac{\ln 7}{\ln x} \ln 53 = \ln \sqrt{x}

\frac{\ln 7 \ln 53}{\ln x} = \frac{\ln x}{2}

{(\ln x)}^{2} = 2 \ln 7 \ln 53

\ln x = \pm \sqrt{2 \ln 7 \ln 53}

x = e^{\pm \sqrt{2 \ln 7 \ln 53}}

x \approx . 0196268 \lor x \approx 50.9508

Commented by David Danile last updated on 04/Jan/20

{c a n}^{'} t w e s o l v e t h i s u s i n g t h e f a c t t b a t

b^{{l o g}_{x} a^{c}} = c ?