SOLUTION: can you please help me solve this equationn? (4)^-3/4 x = 1/2

Question 390812: can you please help me solve this equationn?
(4)^-3/4 x = 1/2

Found 3 solutions by haileytucki, Alan3354, richard1234:
Answer by haileytucki(390)   (Show Source): You can put this solution on YOUR website!
((4)^(-3))/(4x)=(1)/(2)
Expand the exponent (3) to the expression.
(1)/(4^(3))*(1)/(4x)=(1)/(2)
Cubing a number is the same as multiplying the number by itself 3 times (4*4*4). In this case, 4 cubed is 64.
(1)/(64)*(1)/(4x)=(1)/(2)
Multiply (1)/(64) by (1)/(4x) to get (1)/(256x).
(1)/(256x)=(1)/(2)
Since there is one rational expression on each side of the equation, this can be solved as a ratio. For example, (A)/(B)=(C)/(D) is equivalent to A*D=B*C.
1*2=1*256x
Since x is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the equation.
1*256x=1*2
Multiply 1 by 256x to get 256x.
256x=1*2
Multiply 1 by 2 to get 2.
256x=2
Divide each term in the equation by 256.
(256x)/(256)=(2)/(256)
Simplify the left-hand side of the equation by canceling the common factors.
x=(2)/(256)
Simplify the right-hand side of the equation by simplifying each term.
x=(1)/(128)
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Is the x in the exponent?

Answer by richard1234(7193)   (Show Source): You can put this solution on YOUR website!
Since the question is in the "logarithms" section, I'm more likely to interpret it as or . The question is still ambiguous, but in either case, it can be solved by writing 1/2 as , then taking the log base 4 of both sides. It becomes a simple algebra problem there on.
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