Tricky question involving laws of indices

[MadmanMurray]

1. Find value of x if:

4^x-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 I am not quite sure about
Im just assuming that I multiply that -1 by the power inside the brackets but I am not sure if that's right. Anyhow here's what i got
2^2x-2 = 2^-5

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

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

plugging that into the equation doesn't work unfortunately.

 

[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.

 

[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

 

[MadmanMurray]

Ah yeah I didn't see that it came out to 2^-5 in the end thanks. Was my method right? I think they take marks off u for taking roundabout methods.