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### Finding the Base of a Logarithm

```
Date: 06/08/99 at 18:56:00
From: Theodora
Subject: Finding the base of a logarithm

Solve for x:
log (base x) 0.05 = -0.5

I don't get it at all. I couldn't solve it for myself.
```

```
Date: 06/09/99 at 08:01:51
From: Doctor Jerry
Subject: Re: Finding the base of a logarithm

Hi Theodora,

Thanks for your question.

A way that works for this particular problem is:

log_x(5/100) = -1/2

log_x(1/20) = -1/2

-log_x(20) = -1/2

log_x(20) = 1/2.

Now, use the equivalence   log_b(a) = c  is the same as b^c = a:

x^(1/2) = 20.

Now you can figure out x.

- Doctor Jerry, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Logs

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