College Algebra & Trigonometry, 2018a

3.3. SOLVING EXPONENTIAL EQUATIONS 165
3.3 Solving Exponential Equations
Because of the fact that logarithms are exponents, the rules for working with
logarithms are similar to those that govern exponential expressions. One very
helpful rule of equality for working with logarithms is related to the exponential
rule for raising a power to a power. We recall one of the rules of exponents as:
(b x ) y = b x∗y
in other words
(5 2 ) 4 =(5 2 )(5 2 )(5 2 )(5 2 )=5 2∗4 =5 8
In logarithmic notation, this rule works out as:
log b M p = p ∗ log b M
The reason for this comes from the rule for exponents. Let’s say that log b M = x.
Then:
log b M = x
this means that
b x = M
and
(b x ) p =(M) p
so
b p∗x = M p