Question

if 4^x+5=256^2x-3, then x=?​

Answer 1

Answer:

The value of x is 17/7

Step-by-step explanation:

4^(x+5) = 2^[2^(x+5)]     (∵ 4 = 2²)

4^(x+5) = 2^[2(x+5)]     {Using indices (a^[m^n]) = a^(mn)}

1. ∴ 4^(x+5) = 2^(2x+10)

256^(2x-3) = 2^[8^(2x-3)]      (∵256 = 2^8)

256^(2x-3) = 2^[8(2x-3)]     {Using indices (a^[m^n]) = a^(mn)}

2. ∴ 256^(2x-3) = 2^(16x-24)

4^x+5 = 256^2x-3

From (1) & (2),

2^(2x+10) = 2^(16x-24)

If bases are same, powers can be equated.

2x + 10 = 16x - 24

16x - 2x = 24 + 10

14x = 34

x = 34/14

x = 17/7