SOLUTION: How do I convert the formula L=10* Log(I/Io) into exponent form? I already know how to do the decibels (obv with the formula above) but I can't find the I/Io unless I know how t

Question 407091: How do I convert the formula L=10* Log(I/Io) into exponent form?
I already know how to do the decibels (obv with the formula above) but I can't find the I/Io unless I know how to convert that formula into exponent form. Please help :)
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

In general, the is equivalent to . So you want your equation to have the form of thie general logarithmic equation. This means you want to get the 10 out of the way.

There are two way to get the 10 out of the way:

Divide both sides of the equation by 10.
Use a property of logarithms,

I'll do the problem both ways. (They should work out the same.

Dividing by 10:

Now we have the desired form and we can rewrite this in exponential form using the pattern above (and the fact that the base of "log" is 10):

Using the property:

Rewriting in exponential form:

To solve this for we find the 10th root of each side:

may not look like but they are equal. We can replace the radical in with and exponent of 1/10:

And the rule for exponents when raising a power to a power is to multiply the exponents:

which simplifies to:

So both and are correct expressions for .
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