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1. Write the expression as the logarithm of a single number or expression with a coefficient of 1. Assume all variables represent positive
numbers.
log 30 - log 6
A) log 11
B) log 5
C) log 24
D) log
2. Find the value of the expression. log10 10
A) 1
B) -1
C) 0
D) 10
3. Write in logarithmic form. 52 = 25
A) 2 = log25 5
B) 2 = log5 25
C) 5 = log2 25
D) 25 = log5 2
4. Solve the equation for c.
log (7 + p) = log (4c - 5)
A)
B)
C)
D)
5. Solve the equation.
log25 x =
A) 33,554,432
B) 0.00000003
C) 625
D) 5
6. Solve the equation. ln eln x - ln (x - 7) = ln 9
A) 63/8
B)
C) -63/8, 63/8
D) 7, 9
7. Find the value of the expression.
log8
A) 64
B) -3
C) -64
D) 3
8. Write the expression as the logarithm of a single number or expression with a coefficient of 1. Assume all variables represent positive
numbers. ln (5x + 5) + ln (x + 7)
A) ln
B) ln (5x2 + 12x + 35)
C) ln (6x + 12)
D) ln (5x2 + 40x + 35)
9. Classify the function as a linear, quadratic, or exponential. f(x) = 7 ∙ 22x2-7
A) Quadratic
B) Exponential
C) Linear
10. Solve the equation.
log x3 = (log x)3
A) 0, 1
B) 1, 0.138
C) 1, 0.019
D) 1, 3
11. Convert to exponential form.
log5 25 = 2
A) (2)5 = 25
B) (5)25 = 2
C) (25)2 = 5
D) (5)2 = 25
12. Solve the equation. log (x + 9) = 1 - log x
A) -1
B) 1, 10
C) 1
D) -10, 1
13. Evaluate the expression. log7.4 99
A) 2.2959
B) 13.3784
C) 1.9956
D) 0.4356
14. Write the expression as a sum and/or a difference of logarithms with all variables to the first degree.
ln
A)
ln fz - 3 ln z
B) ln f - 3 ln z
C)
ln f -
D) ln f -
ln z
ln z
15. Classify the function as a linear, quadratic, or exponential.
f(x) = 8x + 1
A) Exponential
B) Quadratic
C) Linear
16. Solve the problem. The sales of a mature product (one which has passed its peak) will decline by the function
time in years. Find the sales after
if
where t is
and
A) 9823
B) 114,183
C) 565,550
D) 19,645
17. Use a calculator to evaluate the logarithm.
ln 68
A) 1.8325
B) 25.0923
C) 0.2363
D) 4.2195
18. Solve the exponential equation. 22x = 216
A) 2
B) -8
C) 8
D) 16
19. Write the expression as the logarithm of a single number or expression with a coefficient of 1. Assume all variables represent positive
numbers. log 3 + log 12 - log 4
A) log 9
B) log 16
C) log 7
D) log 11
20. Solve the equation. log9 (x - 5) + log9 (x - 5) = 1
A) -8, 8
B) 8
C)
D) -
,