SOLUTION: log(base x)(1/4) = (-2/3) log(

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Question 717220: log(base x)(1/4) = (-2/3)
log(
Found 3 solutions by josgarithmetic, MathTherapy, greenestamps:
Answer by josgarithmetic(39718) About Me  (Show Source):
You can put this solution on YOUR website!
To making the rendering work, use this sequence of characters:
log
(x,1/4)
=
(-2/3)
and use triple lefthand brackets and triple righthand brackets.


log%28x%2C1%2F4%29=%28-2%2F3%29

If solving for x, transform into, using the fundamental meaning of logarithm,
x%5E%28-2%2F3%29=1%2F4

Now, raise each side to the (-3/2) power.
.
x=1%2F%28%281%2F4%29%5E%283%2F2%29%29
Hopefully that renders properly so you can see all the characters.
= 1%2F%28%28%281%2F4%29%281%2F4%29%281%2F4%29%29%5E%281%2F2%29%29
.
x=8 ?

Answer by MathTherapy(10699) About Me  (Show Source):
You can put this solution on YOUR website!
log(base x)(1/4) = (-2/3)

        log+%28x%2C+%281%2F4%29%29+=+%28-+2%2F3%29
          matrix%282%2C1%2C+%22+%22%2C+x%5E%28-+2%2F3%29+=+1%2F4%29 --------- Converting to EXPONENTIAL form
   -- RAISing each side to the NEGATIVE reciprocal-exponent on x (to the %28-+3%2F2%29%5E%28th%29 power)

              x%5E1+=+%28sqrt%281%2F4%29%29%5E%28-+3%29
               highlight%28x+=+%281%2F2%29%5E%28-+3%29+=+%282%2F1%29%5E3+=+2%5E3+=+8%29

Answer by greenestamps(13292) About Me  (Show Source):
You can put this solution on YOUR website!


log%28x%2C%281%2F4%29%29=-2%2F3

Convert to exponential form:

x%5E%28-2%2F3%29=1%2F4
x%5E%28-2%2F3%29=2%5E%28-2%29

Raise both sides of the equation to the (-3/2) power:

x=%282%5E%28-2%29%29%5E%28-3%2F2%29=2%5E3=8

ANSWER: 8