Question

Solve: $5^x{8}^{\frac{x}{(x+1)}}-100\ge 0$.

Answer 1

$5^x{8}^{\frac{x}{x+1}}-100\ge 0$

$5^x(2^3{)}^{x/x+1}\ge 100$

$5^x{2}^{3x/x+1}\ge 2^2{.5}^2$

$x\ge 2$; $\frac{3x}{x+1}\ge 2$

(By comparing exponents on both sides)

$3x\ge 2x+2$

$x\ge 2$

$\therefore x\ge 2$.