maths: exponent & logarithm - problem solving

4 ^x+1 = 12 ^x-1

(2² )^x+1 = (3. 2 ²) ^x-1

2 ^(2x+2) = 3 ^(x-1). 2 ^(2x-2)

2 ^(2x+2) = 3 ^(x-1)

2 ^(2x-2)

2 ^{(2x+ 2)-(2x-2)} = 3 ^(x-1)

2⁴ = 3 ^(x-1)

16 = 3 <sup>(x-1)

3</sup> log 16 = x-1

³ log 4² + 1 = x

2 ³log 4 + 1 = x