# Tricky question involving laws of indices

1. Jan 2, 2009

1. Find value of x if:

4x-1 = 1/32

3. I know that both 4 and 1/32 can be expressed as powers of 2 so (22)x-1 = 2-5

Heres what im not quite sure about
Im just assuming that I multiply that -1 by the power inside the brackets but im not sure if thats right. Anyhow heres what i got
22x-2 = 2-5

I then eliminated the 2s so Im left with 2x-2 = -5.

doing that in my head I get x = -3/2

plugging that into the equation doesn't work unfortunately.

2. Jan 2, 2009

### HallsofIvy

It looks to me like it works. If x= -3/2 then 2x-2= -3-2= -5 so the left side is 2-5= 1/32, exactly like the right side.

3. Jan 2, 2009

### yeongil

If you were checking in the original equation...
$$4^{-\frac{3}{2}-1}= 4^{-\frac{5}{2}}= (2^{2})^{-\frac{5}{2}}= 2^{-5}= \frac{1}{32}$$

01

4. Jan 3, 2009