Solve: log(2) x – log(x) 8 = 2

We have to solve log(2) x – log(x) 8 =
2

log(2) x – log(x) 8 = 2

use
the property of logarithm: log a^b = b*log a

=>
log(2) x – 3*log(x) 2 = 2

Use the property of logarithm:
log(a)b  = 1/log(b) a

=> log(2) x - 3/log(2) x =
2

=> (log(2) x)^2  - 2*log(2) x - 3 =
0

=> (log(2) x)^2  - 3*log(2) x + log(2) x - 3 =
0

=> (log(2) x)[log(2) x – 3] + 1[log(2) x – 3] =
0

=> [log(2) x  + 1][ log(2) x – 3] =
0

=> log(2) x = -1 and log(2) x =
3

=> x = 1/2  and  x = 2^3 =
8

The solution of the equation is x = 1/2 and
x = 8