Math 172 Calc I and Logarithm Review
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Show all work to receive full credit. Partial credit will be awarded.
Please complete problems on a separate sheet of paper.
Problems 1-3 Differentiate.
1. f (x) = 3x2 (4x − 1)3
2. g(x) =
3x − 3
5x + 6
3. h(x) = 3 cos2 4x
Problems 4-5, Find the indefinite integral or evaluate the definite integral.
Z
12x4 + 6x3 + 8x2 + 3
4.
dx
2x2
5.
Z
3
1
4x(x2 − 1)3 dx
6. Find the equation of the tangent line to the graph of f (x) = 4x2 + x − 1 at the point (3, 38).
7. Find the area of the region bounded by the graphs of f (x) = −3(2x − 1)2 + 27 and y = 0.
Problems 8-11, Express each of the following logarithmic expressions in exponential form.
1
= −5
8. log2 8 = 3
9. log3
243
10. log 31.63 ≈ 1.5
11. ln 5 ≈ 1.6094
Problems 12-15, Express each of the following exponential expression in logarithmic form.
1
12. 53 = 125
13. 4−2 =
16
14. 104 = 10000
15. e3 ≈ 20.0855
16. Write the following as a single logarithm: 2 log x + 3 log y − 4 log(x + 5)
x2 (x − 1)3
17. Write the following as a sum/difference of logarithms. Express powers as factors: ln √
x−4
18. Simplify the expression: e2 ln 3+4 ln 5
Problems 19-20, Solve each equation. State the EXACT and approximate solution
19. 34x−1 = 5
20. ln x + 2 ln 5 = 3