Answer:
x = 3
Step-by-step explanation:
Given:
[tex] \implies \rm 3 {}^{x} + {3}^{x} = 54[/tex]
To Find:
Solution:
We could re-write 3^x+3^x as:
[tex] \implies \: 2(3 {}^{x} ) = 54[/tex]
Divide both sides by 2
[tex] \implies \cfrac{2(3 {}^{x}) }{2} = \cfrac{54}{2} [/tex]
[tex] \implies \: 3 {}^{x} = 27[/tex]
Take logarithm on both sides
[tex] \implies \: \log(3 {}^{x} ) = \log(27)[/tex]
[tex] \implies \: x \times \log(3) = \rm \: log \: (27)[/tex]
[tex] \implies \: x = \cfrac{ \log(27)}{ \log \:(3)} [/tex]
[tex] \implies \boxed{x = 3}[/tex]
Hence, x = 3 .
