Find x.

2^3x = 8^2x+1

The above given equation can also be written as,

2^3x = ((2)³)^{2x + 1} ∵ 2³ = 8

As we know by the laws of exponent, that,

(a^m)ⁿ = a^mn

⇒ 2^3x = 2^{3(2x + 1)}

As the bases are same so the exponents can be equated,

⇒ 3x = 3(2x + 1)

⇒ x = 2x + 1

⇒ x = -1

∴ Value of x =-1