Question

Find the value of $x$, if $3^x-3^{x-1}=54$

• A. 2
• B. 4
• C. 1
• D. 3

Answer 1

The correct option is B 4

$3^x-3^{x-1}=54$
$\Rightarrow 3\times 3^{x-1}-3^{x-1}=54$
$\Rightarrow (3-1)\times 3^{x-1}=54$
$\Rightarrow 2\times 3^{x-1}=54$
$\Rightarrow 3^{x-1}=27$
$\Rightarrow 3^{x-1}=3^3$

As bases are equal on both the sides, we can equate the powers.
$\Rightarrow x-1=3$
$\Rightarrow x=4$