# Solve the equation: `log_(1/2)(log_4x-3*log_2x+4)=-1`

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### 3 Answers

The equation `log_(1/2)(log_4x-3*log_2x+4)=-1` has to be solved for x.

`log_(1/2)(log_4x-3*log_2x+4)=-1`

=> `log_4x-3*log_2x+4 = (1/2)^-1`

=> `log_4x-3*log_2x+4 = 2`

=> `(log_2x)/2 - 3*log_2x + 2 = 0`

=> `log_2x - 6*log_2x + 4 = 0`

=> `-5*log_2x = -4`

=> `log_2x = 4/5`

=> `x = 2^(4/5)`

**The solution of the equation is `x = 2^(4/5)` **

## log1/2(log4x-3log2x+4)=-1

log4x-3log2x+4=2 log2x=t ---- log2x=t1

t2-3t+4=2 log2x=2

t2-3t+4-2=0 t1,2=3+or-1/2 ** x=4**

t2-3t+2=0 t1=2 log2x=t2

D=b2-4ac t2=1 log2x=1

D=9-4*2 **x=2**

D=9-8

D=1

accurate solutions in my book are X = 4 and X = 2

but thanks