Question

For \[y=x^{\sin x}\], \[x>0\], what equation results after taking logarithm on both sides?

Options

• \[\log y=x\log(\sin x)\]

• \[\log y=\sin x+x\]

• \[\log y=\frac{\log x}{\sin x}\]

• \[\log y=\sin x\log x\]

Answer 1

For \[x^{\sin x}\], the logarithm rule gives \[\log(x^{\sin x})=\sin x\log x\]. The condition \[x>0\] ensures that \[\log x\] is defined.