Logarithms are considered the inverse or opposite operations to exponents, just as subtraction is the inverse to to addition or square rooting is the inverse to squaring.
For example, suppose we have the exponential expression , which we know will equal 8. Now, suppose we want to do the inverse operation and go from the value 8 to the exponent 3 with a base of 2. We could do the inverse operation by using logarithms and write , which is read "logarithm of 8 base 2 is equal to 3".
- In order words, if we have an exponential equation:
- we can write an equivalent logarithmic equation:
What about exponential equations in the form ? It might seem harder to solve for x in this case because there is no whole number exponent that will give us the value of 932 with a base of 10. However, if we simply rewrite the equation as an logarithmic equation , we can find quite easily with a calculator that x is about 2.969.
To look at some more examples of switching between exponential and logarithmic equations:
A More Mathematical Description