Question

x^(sqrt(log(x)))=10^8

Answer 1

\[x^{\sqrt{\log(x)}}=10^{8}\]

Answer 2

I would start by taking log( ) of both sides

Answer 3

\[x ^{\sqrt{\log(x)}}=10^8\]
\[\log \left( x ^{\sqrt{logx}} \right)=\log \left( 10^8 \right)\]
\[\sqrt{logx}logx=8\log10\]
\[\left( logx \right)^{\frac{ 3 }{ 2 }}=8*1=8\]
\[\log x=8^{\frac{ 2 }{ 3 }}=\left( 2^3 \right)^\frac{ 2 }{ 3 }=2^2=4,x=10^4\]

Answer 4

perfect!

Answer 5

thanks guys