Question

a) $\sqrt[x]{27^{2x-1} } = \sqrt{9^{2x-1} }$

b)$5* 4^x}-11* 6^{x} +2* 9^{x}=0$

Answer 1

27^[(2x-1)/x]=9^(2x-1)

(3^3)^[(2x-1)/x]=(3^2)^(2x-1)

3^[3*(2x-1)/x]=3^[2*(2x-1)]

3*(2x-1)/x=2*(2x-1)

6x-3=4x^2-2x

4x^2 -8x+3=0

(2x-3)(2x-1)=0

x={1/2;2/3}