Just some hard indices problems I need help with, I have no idea how to go about these:

find n:

(1/4)^n=8

(125/8)^n=25/4

(81/16)^n=32/243

81^2n-1=27^3n+1

16^2-n = (1/4)n+1

thanks, as I can't seem to find the right method

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- Sep 4th 2010, 01:54 AMGoodLuckMeIndices help needed
Just some hard indices problems I need help with, I have no idea how to go about these:

find n:

(1/4)^n=8

(125/8)^n=25/4

(81/16)^n=32/243

81^2n-1=27^3n+1

16^2-n = (1/4)n+1

thanks, as I can't seem to find the right method - Sep 4th 2010, 03:28 AMSoroban
Hello, GoodLuckMe!

The procedure is:

. . Express all exponential in the same base.

. . Equate exponents.

. . Solve for

I'll do the last one.

Quote:

We note that: .

So we have: .

. . . . . . . . . .

. . . . . . . . . . .

. . . Then: . .

. . . . . . . . . . .

. . . . . . . . . . . . .

- Sep 4th 2010, 05:54 AMjgv115
I'll do the first one (another example)

Note that

So...

Make the bases the same:

Now cancel

:) - Sep 5th 2010, 12:07 PMGoodLuckMe
thanks-that's wonderfully helpful :) now I've got the method It should be alot easier.

much appreciated.