solve..............

Question

Solve ?256?^x=?64?^(2-x)

Answer 1

Alternatively,

 

Note that 256 = 2⁸ and 64 = 2⁶.

 

So we could simplify 256^x=64^(2-x) to

(2⁸)^x = (2⁶)^2-x

2^8x = 2^12-6x

8x = 12 - 6x

x = 12/14

x = 6/7

 

Answer 2

256^x = 64^2-x

Take log4 of both sides:

log₄ 256^x = log₄ 64^2-x


x (log₄ 256) = (2-x) (log₄ 64)

x (4) = (2-x)(3)

4x = 6 - 3x

 

7x = 6

 

x = 6/7