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

Asked on by emmmaa

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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)`

elmee | Student, Grade 10 | (Level 1) Honors

Posted on

## 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

emmmaa | Student, Grade 10 | (Level 1) Honors

Posted on

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

We’ve answered 319,199 questions. We can answer yours, too.