1. To solve a logarithmic equation, rewrite the equation in exponential form and solve for the variable.
Example 8: If , and a and b are positive, show that
no matter what positive value for the base is used for the logarithms (but
it is understood that the same base is used throughout).
Solution:
All we did to the quantity with the brackets on the left side of the equation is raise it to a net power of 1. Remember that . All we did to the right side was simplify it using Logarithm Rules 1 and 3.
or .
can be simplified using Logarithmic Rules 1 and 3:
If you would like to review another example, click on Example.
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Author: Nancy Marcus