if 4^x - 4^x-1 = 24, then find value of x. please explain.

Answer 1

4 ^ ( x - 1 ) = 4 ^ x / 4 ^ 1 = 4 ^ x / 4

4 ^ x - 4 ^ ( x - 1 ) = 24

4 ^ x - 4 ^ x / 4 = 24

4 * 4 ^ x / 4 - 4 ^ x / 4 = 24

3 * 4 ^ x / 4 = 24 Multiply both sides by 4

3 * 4 ^ x = 96 Divide both sides by 3

4 ^ x = 32

x * log ( 4 ) = log ( 32 ) Divide both sides by log ( 4 )

x = log ( 32 ) / log ( 4 )

x = 3.465736 / 1.386294

x = 2.5

x = 5 / 2

log is " Natural logarithm " ( Logarithm with base e )