Name___________________________________________
Honors Algebra I
Exponential and Logarithmic Functions Review
Write each equation in its equivalent exponential form
1.

1
 log 343 7
3
2.
log 1 64  x
2

Write each equation in its equivalent logarithmic
form.
3.
6 x  216
4.

13y  874

Evaluate each expression WITHOUT a calculator. If evaluation is not possible, state the
reason.
5.

log 6
1
36
9.
log 6 3 6 2
log 4 410


11.
log 3 log 3 1
log 4 (16)
10.
log 3 (log 5 5)
13.
10 log4 x

12.

7.


8.

6.
log 4 256
5log5 5
2

Use the properties of logarithms to expand each logarithmic expression as much
possible, Where possible, evaluate the logs.
14.
36x 3 
log  2 
 y 

15.
xy 2 
log 
 64 

16.
(3xy) 3 
log
2 
(9xz) 

Use the properties of logarithms to condense each logarithmic expression into a single
logarithm.
17.

7log x  3log y  4log z
18.

1
log 4 x  log 4 y  log 4 z
3
Solve each exponential equation. If necessary, round t0 the nearest hundredths place.
19.
2 4 x 2  64

9 x 2  27 x
20.

21.
3x 4  7 2x 1

Solve each logarithmic equation. Round all answers to the nearest hundredths place.
22.
log 4 (2x  5)  3


24.
log 3 (x 1)  log 3 (x  2)  2
25.
log( 2x 1)  log( x  3)  log( x  5)


23.
3 4log( 2x) 15
26.
How long, the nearest tenth of a year, will it take $30,000 to triple in value at
7.5% annual interest compounded monthly?
Compounded continuously?