Chapter 1 | Functions and Graphs
103
Figure 1.47 Graphs of y = log b ( x ) are depicted for b =2, e , 10.
Before solving some equations involving exponential and logarithmic functions, let’s review the basic properties of logarithms.
Rule: Properties of Logarithms If a , b , c >0, b ≠1, and r is any real number, then 1.
log b ( ac ) = log b ( a )+log b ( c ) (Product property)
⎛ ⎝ a c
⎞ ⎠ = log b ( a )−log b ( c )
2. 3.
log b
(Quotient property) (Power property)
r ) = r log
log b ( a
b ( a )
Example 1.36 Solving Equations Involving Exponential Functions
Solve each of the following equations for x . a. 5 x =2 b. e x +6 e − x =5
Solution a. Applying the natural logarithm function to both sides of the equation, we have ln5 x = ln2.
Using the power property of logarithms,
x ln5= ln2.
Therefore, x = ln2/ln5. b. Multiplying both sides of the equation by e x , we arrive at the equation e 2 x +6=5 e x .
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