# I have a variable as an exponent, how do I isolate it from everything else?

## Homework Statement

.75 = 1 - (1 - p)^n
I want to get the n alone, and find n in terms of p.

## The Attempt at a Solution

I simplified it to this:
1 - p = (.25)^(1/n)
Basically, I just moved numbers around. I do not know how to get the n by itself without dragging along a number.

Thanks!

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Mark44
Mentor

## Homework Statement

.75 = 1 - (1 - p)^n
I want to get the n alone, and find n in terms of p.

## The Attempt at a Solution

I simplified it to this:
1 - p = (.25)^(1/n)
Basically, I just moved numbers around. I do not know how to get the n by itself without dragging along a number.

Thanks!
Take the log of both sides.

.75 = 1 - (1 - p)n
==> .25 = (1 - p)n
==> ln(.25) = ln[(1 - p)n]

Using one of the properties of logarithms, you can work with the right side to eventually isolate n.

Char. Limit
Gold Member
Have you tried logarithms?

Logarithms would be the best way to get change the variable from a constant to a coefficient. Any logarithm will work, whether it be the standard log10, the natural log ln, or any other one.

log(ax) = x*log(a)

Here's an example on how to use this property:

3.2x = 10.24
ln(3.2x) = ln(10.24)
Using the property mentioned:
x*ln(3.2) = ln(10.24)
x*1.1631 = 2.3263
x = 2.3263/1.1631
x = 2

Note (again) that it doesn't matter whether you choose the ln or log10 or log12345, so long as you use the logarithm on BOTH sides of the equation and then use the mentioned property you'll be fine.