Question

Solve 81x = 27 ^x + 2.

Answer 1

Note that 81 = 3^4 and 27 = 3³. Then, we have..

3^(4x) = 3^(3(x + 2))
3^(4x) = 3^(3x + 6)

Set the exponents equal to each other..

4x = 3x + 6

Subtract both sides by 3x...

4x - 3x = 3x - 3 + 6

So x = 6 [D]

I hope this helps!