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Classwork
Find an equation for, f
1
( x) , the inverse function of the following one-to-one function.
a. f ( x)  ( x  1) 3  1
b. g ( x) 
4
x2
c. f ( x) 
 3x  1
2x  5
Rewrite each logarithm so that the expression contains no logarithms of products,
quotients or powers.
a. log100 x 2 
 64 
b. log 4  5 
x 
 z10 x 
c. log 5  13 3 
5 y 
Write the following expression as a single logarithm.
a. log 4 2  log 4 8
b. 2 ln x  5 ln x  ln x
1
c. log v  log z  4 log w
3
d.  log 2 ( x 2  81)  log 2 ( x  9)
Use natural logarithms to rewrite log17 3 .
Use common logarithms to rewrite log 9 11 .
Section 5.4 – Properties of Logarithms
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Write each equation in its equivalent exponential form.
a. 3  log 7 x
b. 2  log b 25
c. log 2 32  5
Write each equation in its equivalent logarithmic form.
a. 2 5  x
b. e y  33
c. 38  x
Evaluate.
a. log 10
b. log   
e
c. 6 log6 27
d. e ln 100
Section 5.4 – Properties of Logarithms
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