All High School Math Resources
Example Question #43 : Understanding Logarithms
is equivalent to . In other words, we know the base and we know the result; we're looking for the exponent to get us there.
The best way to solve a problem like this is to use a base change. can also be solved as . The great part of this is that when you use the function on your calculator, it's already set to a base of .
Go ahead and plug in the numbers from the problem to solve.
Example Question #1 : Using Natural Log And Log Base 10
Most of us don't know what the exponent would be if and unfortunately there is no on a graphing calculator -- only (which stands for ).
Fortunately we can use the base change rule:
Plug in our given values.
Example Question #3 : Understanding Logarithms
Based on the definition of logarithms, what is ?
For any equation , . Thus, we are trying to determine what power of 10 is 1000. , so our answer is 3.