Logarithmic and Exponential Functions – Precalculus
Solve the equations.
1. Solve 4x  19 . Express answers in exact form and as a decimal rounded to three decimal places.
2. Solve 5x  17 . Express answers in exact form and as a decimal rounded to three decimal places.
3. Solve 54 x  3 . Express answers in exact form and as a decimal rounded to three decimal places.
Graph the exponential functions.
4. Graph y  4 x .
x
1
5. Graph y    .
4
x
1
6. Graph y     1 .
2
Find the values of logarithmic expressions.
7. Use the properties of logarithms to find the exact value of log3 354 .
8. Find the value of logarithmic expression log 2 4 .
9. Find the value of logarithmic expression log 5
1
.
25
10. Find the value of logarithmic expression log 2
1
.
16
Write logarithm expressions.
11. Write log 8 x  log 8 y as the logarithm of a single expression.
 x4 
12. Write log 7   as a sum or difference of a multiple of logarithms.
 y 
Solve the equations.
13. Solve log8 7  log8 x  0 .
14. Solve log6 x  log 6  x  9   2 .
15 Solve log4  x2  3x   1 .
16. Solve log 2 x  log 2  5 x  3  1 .
17. Solve log b x  log b 5  log b 3 .
1
18. Solve 2 log b 3  log b y  log b 25 .
2
Answer key
1. Exact: x 
log19
; Rounded: x  2.124
log 4
3. Exact: x 
log 3
; Rounded: x  0.171
4log 5
6.
7. 54
12. 4 log 7 x  log 7 y
17. x  15
18. y 
13. x 
5
9
2. Exact: x 
4.
8. 2
1
7
log17
; Rounded: x  1.760
log 5
5.
9. 2
14. x  12
10. 4
15. x  4, 1
x
11. log8  
 y
16. x 
2
5