5.5 Exponential and Logarithmic Equations

Hey Guys! Its bout to be a party

When you are solving an equation with variables as exponents and constants as the base we can "take the log of both sides" to make it easier to solve. For ex:

by then using a calculator you would come to the answer

natural logarithms could have also have been used to obtain

These are both alternatives to using logarithmic form or "the key to everything" as in 5.3

a quick recap

using this method you would have come to the equation

most calculators do not have a key so you would then be left with this as your simplified answer.

This is why the new "take the log of both sides" technique is useful

Which leads to the next topic. When dealing with an equation that has a logarithmic base other than e or 10 you can use this handy theorem called the: Change of Base Formula

If

and if a and b are pos real numbers different from 1, then

When using this Formula REMEMBER

AND

ARE NOT TRUE

Also as a refresher

And

Now that we know the Change of Base Formula We can apply it to problems such as the first example.

Using "The Key to Everything" you get

APPLY

to get

Just as before

A little more practice

you can also use it in exponential equations