Review Exam 4
1) Rewrite the expression as a sum or difference of logarithms.
3 x5 
log 5  4 2 
 y z 
2) Rewrite the expression as a single logarithm
1
2
1
log 3 ( x)  log 3 ( y  1)  log 3 ( z )
2
3
4
3) Simplify each expression
a. 10 log 2
b.
log 4
1
64
c. e ln 2ln 3
4) Solve each exponential equation.
a) 2 x 1  2 x 
1
8
b) 3(2x1)  6 x
5) Solve each logarithmic equation.
a)
1
log( x  1)  3
2
b) log2(x) + log2(x + 2) = 3
6) Graph and state domain and range of f(x) = lnx.
7) Graph and state domain and range of f(x) = log 1 x
3
8) Graph and state domain and range of f(x) = 3 x
9) Graph and state domain and range of f(x) = e x
10) An earthquake on December 16, 1811, in New Madrid, Missouri, had the seismographic reading of
105 mm. What would have been its magnitude?