Question

The value of $x$ which satisfies $3^{2x-1}=27$ is .

Answer 1

$\underset{–}{\text{Need to find:}}$ Value of $x$ which satisfies the exponential equation $3^{2x-1}=27$

$3^{2x-1}=27$
$\Rightarrow 3^{2x-1}=3^3(\because 27=3\times 3\times 3=3^3)$

In the above exponential equation, the base $\left(3\right)$ is same. Hence, for L.H.S=R.H.S, the powers must be same.

$\Rightarrow 2x-1=3$
$\Rightarrow 2x-1+1=3+1$
$\Rightarrow 2x=4$

$\Rightarrow \frac{2x}{2}=\frac{4}{2}$

$\Rightarrow x=\frac{4}{2}$

$\Rightarrow x=\frac{2\times 2}{2}$
$\Rightarrow \underset{–}{x=2}$

$\therefore$ The value of $x$ which satisfies the exponential equation $3^{2x-1}=27$ is $\underset{–}{2}$.