Question

# X^{frac{logx+5}{3} } =10^{5+logx}

Solution

x^{frac{log+5}{3} }=10^{5+logx}⇒x^{frac{logx+15}{3} }=15^{5}.10^{logx}=10^5.x⇒(frac{logx+5}{3})(logx) =(5+logx)(log_{10}10 )5+log_{x} ⇒(logx)^2+5logx=15+3logx⇒(logx)^2+2logx-15=0⇒(logx)^2+5logx-3logx-15=0⇒(logx+5)(logx-3)=0⇒logx=3 (∵ logx≠-5)

⇒ x=10^3=1000