Question

find x
$3 ^{x} + 3 ^{x - 1} = 108$
​

Answer 1

Answer:

x = 4

Step-by-step explanation:

$given \: 3 {}^{x} + 3 {}^{x - 1} = 108 \\ 3 {}^{x} + \frac{3 {}^{x}}{3} = 108 \\ 3 {}^{x}(1 + \frac{1}{3}) = 108 \\ 3 {}^{x}( \frac{4}{3}) = 108 \\ 3 {}^{x} = 108 \times \frac{3}{4} = \frac{324}{4} = 81 \\ 3 {}^{x} = 3 {}^{4} \\ hence \: x = 4$