Find the value of $x$ (without hit and trial) from the equation $x^2(\log_{10} x )^5 = 100$.
Solving few steps I got $x= 10^{({\frac{x}{10}})^5} $.
[Math] How to solve the equation $x^2(\log_{10} x )^5 = 100$
logarithms
logarithms
Find the value of $x$ (without hit and trial) from the equation $x^2(\log_{10} x )^5 = 100$.
Solving few steps I got $x= 10^{({\frac{x}{10}})^5} $.
Best Answer
$log_{10}x=y\\ \implies 10^y=x\\ \implies x^2=10^{2y}$
The equation will then become
$10^{2y}y^5=100$
One solution that I see is $y=1$, which will give $x=10$. Why do you wish to solve this equation without hit-and-trial method?