Question

Solve:

$\frac{e^{5\log x}-e^{4\log x}}{e^{3\log x}-e^{2\log x}}$

Answer 1

$=\frac{e^{5logx}-e^{4logx}}{e^{3logx}-e^{2logx}}$

$=\frac{e^{log{x}^5}-e^{log{x}^4}}{e^{log{x}^3}-e^{log{x}^2}}$ $(\because alo{g}_{e}b=log{b}^a)$

$=\frac{5-4}{3-2}=1$

$(\because e^{lo{g}_{e}x}=x)$.