3^x+3^x =54 what's the value of x ?

Question

asked Jul 26, 2023 140 views

2 Answers

Mitchf · Answer 1 · 2023-07-30T15:02:50+0000

Answer:

x = 3

Explanation:

Given:

$\implies \rm 3 {}^(x) + {3}^(x) = 54$

To Find:

Solution:

We could re-write 3^x+3^x as:

$\implies \: 2(3 {}^(x) ) = 54$

Divide both sides by 2

$\implies \cfrac{2(3 {}^(x)) }{2} = \cfrac{54}{2}$

$\implies \: 3 {}^(x) = 27$

Take logarithm on both sides

$\implies \: \log(3 {}^(x) ) = \log(27)$

$\implies \: x * \log(3) = \rm \: log \: (27)$

$\implies \: x = \cfrac{ \log(27)}{ \log \:(3)}$

$\implies \boxed{x = 3}$

Hence, x = 3 .