Question

Solve: $x^{\log 5}=50$

log is to the base of 10.

$Ifx=10\times 3^k$

Then value of k=

Answer 1

Given: $x^{\log 5}=50$

$\log x^{\log 5}=\log 50$ [We can write $log50=log(5\times 10)=log5+log10$ ]

$\log x=\frac{\log 5+1}{\log 5}$ [$log10=1$]

$\log 5\times \log x=\log 5+1$

$x={10}^{1+\frac{1}{\log 5}}=270$