8^x = 1/32, find x?

I don't want the answer I just want to know how to go about answering this... Is there a simple method I could do to figure x out?

Thanks

Original post by funkybinoculars

I don't want the answer I just want to know how to go about answering this... Is there a simple method I could do to figure x out?

Thanks

I suggest you take logs :smile:

1/32 = 1/(2)^5
1/(2)^5 = (2)^-5
now, 8 = 2^3
so, 8^x = ((2)^3)^x =2^3x
Hence,
2^3x = 2^-5
equating powers,
3x = -5
x = -5/3

Original post by funkybinoculars

I don't want the answer I just want to know how to go about answering this... Is there a simple method I could do to figure x out?

Thanks

Use your log rules

log8(1/32) = x

Solve from there :smile:

(2^{-3})^{x} = 2^{-5}

Use your log rules

log8(1/32) = x

Solve from there :smile:

I'm revising logs right now lol but I think I need to know how to solve it without putting this on the calculator to figure it out.

Original post by funkybinoculars

I'm revising logs right now lol but I think I need to know how to solve it without putting this on the calculator to figure it out.

You need to turn both sides into powers of two then you can put the indices equal to each other.

1/32 = 1/(2)^5
1/(2)^5 = (2)^-5
now, 8 = 2^3
so, 8^x = ((2)^3)^x =2^3x
hence,
2^3x = 2^-5
equating powers,
3x = -5
x = -5/3

thank you!! :smile:

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