Answer:
[tex]x=\frac{1}{4}[/tex]
Step-by-step explanation:
[tex]81^{x+1}+3^{4x}=246[/tex]
[tex]81=3^4[/tex]
Rewrite equation: [tex]3^{4\left(x+1\right)}+3^{4x}=246[/tex]
[tex]3^{4\left(x+1\right)}=3^{4x}\times 3^4[/tex]
[tex]3^{4x}\times 3^4+3^{4x}=246[/tex]
Factor out [tex]3^{4x}[/tex]:
[tex]3^{4x}\left(3^4+1\right)=246[/tex]
Divide both sides by [tex](3^4+1)[/tex]:
[tex]\frac{3^{4x}\left(3^4+1\right)}{3^4+1}=\frac{246}{3^4+1}[/tex]
[tex]3^{4x}=\frac{246}{3^4+1}[/tex]
[tex]3^{4x}=\frac{246}{82}[/tex]
[tex]3^{4x}=3[/tex]
Anything to the power of 1 is itself. Hence,
[tex]4x=1\\[/tex]
[tex]x=\frac{1}{4}[/tex]
