Question

Solve

$\log x\sqrt{5}+\log x5x=\frac{9}{4}+{\log }^{2}x\sqrt{5}$

Answer 1

$\log x\sqrt{5}+\log x5x=\frac{9}{4}+{\log }^{2}x\sqrt{5}$

$\log x\sqrt{5}+\log x5x=\frac{9}{4}+2\log x\sqrt{5}$

$\log x5x=\frac{9}{4}+\log x\sqrt{5}$

$\log x5x-\log x\sqrt{5}=\frac{9}{4}$

$\log \frac{x5x}{x\sqrt{5}}=\frac{9}{4}$

$\log \sqrt{5}x=\frac{9}{4}$