Math Help
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Student: Kiare Mays Date: 06/15/20
Instructor: Valery Shemetov Course: MTH154 – Quantitative Reasoning (with MCR4)
Assignment: Section 7.1 Homework
A certain town's population is growing according to the following equation. Answer parts (a) through (c).
P = 7,800 • (1.068)t
(a) To find how long it will take for the population, P, to , substitute for P.triple (Type an integer or a decimal.)
(b) We are looking at the time, t, which solves the equation: . Fill in the following table.3 = (1.068)t
t 1.068 t
14 15 16 17 18 19
(Type integers or decimals rounded to four decimal places as needed.)
(c) The time it takes to is closest to what integer value of t in the table above?triple
The time it takes to is closest to t .triple =
Solve for x.
3x = 27
The solution is x .= (Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed.)
Solve for x.
log x = 610
x =
Solve for x.
log x = 4.610
x = (Round to two decimal places as needed.)
5. Evaluate logarithms without using a calculator by rewriting them in exponential form. Answer parts (a) through (d).
(a) Rewrite y as an exponential. Select the correct choice below and fill in the answer box within your choice.log 497 =
A. 49 = 7
B. 749 =
C. 7 = 49
(b) Solve the equation y.log 497 =
log 497 = (Type an integer or a decimal rounded to two decimal places as needed.)
(c) Rewrite y as an exponential. Select the correct choice below and fill in the answer box within your choice.log 17 =
A. 1 = 7
B. 7 = 1
C. 71 =
(d) Solve the equation y.log 17 =
log 17 = (Type an integer or a decimal rounded to two decimal places as needed.)
6. Evaluate logarithms without using a calculator by rewriting them in exponential form. Answer parts (a) through (d).
(a) Rewrite y as an exponential. Select the correct choice below and fill in the answer box within your choice.ln e − 6 =
A. − 6e =
B. 2 = e − 6
C. e = e − 6
(b) Solve the equation y.ln e − 6 =
ln e − 6 = (Type an integer or a decimal.)
(c) Rewrite y as an exponential. Select the correct choice below and fill in the answer box within your choice.ln e 19 =
A. 2 = e 19
B. 19e =
C. e = e 19
(d) Solve the equation y.ln e 19 =
ln e 19 = (Type an integer or a decimal.)
7. Evaluate logarithms without using a calculator by rewriting them in exponential form. Answer parts (a) through (d).
(a) Rewrite y as an exponential. Select the correct choice below and fill in the answer box within your choice.log 0.0001 =
A. 103 =
B. 10 = 0.0001
C. 0.0001 = 10
(b) Solve the equation y.log 0.0001 =
log 0.0001 = (Type an integer or a decimal.)
(c) Rewrite y as an exponential. Select the correct choice below and fill in the answer box within your choice.
log 1,000,000 =
A. 10 = 1,000,000
B. 1,000,000 = 10
C. 101,000,000 =
(d) Solve the equation y.log 1,000,000 =
log 1,000,000 = (Type an integer or a decimal.)
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Evaluate logarithms using properties of logarithms. Answer parts (a) through (f).
(a) Rewrite the following as a power of 10.
10 • 103 5 = 10 (Simplify your answer.)
(b) Solve the equation y.log 103 • 105 =
log 103 • 105 = (Simplify your answer.)
(c) Rewrite the following as a power of 10.
10 ÷ 103 5 = 10 (Simplify your answer.)
(d) Solve the equation y.log 103 ÷ 105 =
log 103 ÷ 105 = (Simplify your answer.)
(e) Rewrite the following as a power of 10.
103 5
= 10 (Simplify your answer.)
(f) Solve the equation y.log 103 5 =
log 103 5 = (Simplify your answer.)
Using the approximation , find each of the following without a calculator.log 610 ≈ 0.778
a. b. c. d. log 1036 log 10600 log 10 1 36 log 100.6
a. log 1036 = (Simplify your answer. Type an integer or decimal rounded to three decimal places as needed.)
b. log 10600 = (Simplify your answer. Type an integer or decimal rounded to three decimal places as needed.)
c. log 10 1 36 =
(Simplify your answer. Type an integer or decimal rounded to three decimal places as needed.)
d. log 100.6 = (Simplify your answer. Type an integer or decimal rounded to three decimal places as needed.)
10. Evaluate the following expressions.
a. 10 104 × 7 b. 10 109 × − 5 c. 109
103 d.
104
10 − 2
a. (Simplify your answer. Type your answer using exponential notation.)10 104 × 7 =
b. (Simplify your answer. Type your answer using exponential notation.)10 109 × − 5 =
c. (Simplify your answer. Type your answer using exponential notation.) 109
103 =
d. (Simplify your answer. Type your answer using exponential notation.) 104
10 − 2 =