Question

Solve for x is belong to real no.

4^x-10.2^x-1=24

Answer 1

Hi ,

4^x - 10 × 2^x-1 = 24

2^2x - 10 × ( 2^x/2 ) - 24 = 0

( 2^x )² - 5 × 2^x - 24 = 0

( 2^x )² - 8 × 2^x + 3 × 2^x - 24 = 0

2^x ( 2^x - 8 ) + 3 ( 2^x - 8 ) = 0

( 2^x - 8 ) ( 2^x + 3 ) = 0

Therefore ,

2^x - 8 = 0 or 2^x + 3 = 0

2^x = 8

2^x = 2³

x = 3

I hope this helps you.

: )