Question

The roots of the equation $2^{x+2}{27}^{\frac{x}{x-1}}=9$ are given by

• A. $1-{\log }_{2}3,2$
• B. $\log \frac{2}{3},1$
• C. $-2,-2$
• D. $-2,1-\frac{\log 3}{\log 2}$

Answer 1

The correct option is C $-2,-2$

$2^{x+2}{.27}^{\frac{x}{x-1}}=9$

or, $2^{x+2}{.3}^{\frac{3x}{x-1}}=2^0{.3}^2$

Comparing the powers of $2$ and $3$ both sides we get,

$x=-2$ and $\frac{3x}{x-1}=2\Rightarrow x=-2$.

Required roots are $-2,-2$.