Question

X
81** *34*=246

`81x + 1 + 3{4x } = 246`
​

Answer 1

`x=(1)/(4)`

Explanation:

`81^(x+1)+3^(4x)=246`

`81=3^4`

Rewrite equation:
`3^(4\left(x+1\right))+3^(4x)=246`

`3^(4\left(x+1\right))=3^(4x)* 3^4`

`3^(4x)* 3^4+3^(4x)=246`

Factor out
`3^(4x)`:

`3^(4x)\left(3^4+1\right)=246`

Divide both sides by
`(3^4+1)`:

`(3^(4x)\left(3^4+1\right))/(3^4+1)=(246)/(3^4+1)`

`3^(4x)=(246)/(3^4+1)`

`3^(4x)=(246)/(82)`

`3^(4x)=3`

Anything to the power of 1 is itself. Hence,

`4x=1\\`

`x=(1)/(4)`