Question

Solve for x : 2^5x-1 = 4 2^{3x + 1}

Answer 1

 2^5x-1 = 4  x 2^{3x + 1}
⇒  2^5x-1 = 2² x 2^{3x + 1}
⇒  2^5x-1 = 2^{2 + 3x + 1}
⇒  2^5x-1 = 2^{3x + 3}
We know that if bases are equal, the powers are equal
⇒ 5x - 1 = 3x + 3
⇒ 5x - 3x = 3 + 1
⇒ 2x = 4
⇒ x = `4/2`
⇒ x = 2.