Ch. 4 - Inverse, Exponential, and Logarithmic Functions
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- Find the [H_3O^+] for each substance with the given pH. Write answers in scientific notation to the nearest tenth. See Example 2(b). soda pop, 2.7
Problem 33
- Solve each equation. In Exercises 11–34, give irrational solutions as decimals correct to the nearest thousandth. In Exercises 35-40, give solutions in exact form. See Examples 1–4. 5(1.015)^(x-1980) = 8
Problem 33
Problem 34
Graph each function.
- Solve each equation. In Exercises 11–34, give irrational solutions as decimals correct to the nearest thousandth. In Exercises 35-40, give solutions in exact form. See Examples 1–4. e^2x - 6e^x + 8 = 0
Problem 35
- Graph each function. See Example 2. ƒ(x) = 4^-x
Problem 35
- Solve each equation. log￬9 x = 5/2
Problem 35
- Find the [H_3O^+] for each substance with the given pH. Write answers in scientific notation to the nearest tenth. See Example 2(b). beer, 4.8
Problem 35
- Solve each equation. In Exercises 11–34, give irrational solutions as decimals correct to the nearest thousandth. In Exercises 35-40, give solutions in exact form. See Examples 1–4. 2e^2x + e^x = 6
Problem 37
Problem 37
Graph each function. See Example 2. ƒ(x) = 2|x|
- Solve each equation. log￬1/2 (x+3) = -4
Problem 37
- Suppose that water from a wetland area is sampled and found to have the given hydronium ion concentration. Determine whether the wetland is a rich fen, a poor fen, or a bog. See Example 3. 2.49*10^-5
Problem 37
- Solve each equation. log￬1/3 (x+6) = -2
Problem 38
Problem 38
Graph each function.
- Solve each equation. In Exercises 11–34, give irrational solutions as decimals correct to the nearest thousandth. In Exercises 35-40, give solutions in exact form. See Examples 1–4. 5^2x + 3(5^x) = 28
Problem 39
- Suppose that water from a wetland area is sampled and found to have the given hydronium ion concentration. Determine whether the wetland is a rich fen, a poor fen, or a bog. See Example 3. 2.49*10^-2
Problem 39
Problem 40
Use the definition of inverses to determine whether ƒ and g are inverses.
- Solve each equation. Give solutions in exact form. See Examples 5–9. 5 ln x = 10
Problem 41
- Solve each equation. 3x - 15 = log￬x 1 (x>0, x≠1)
Problem 41
- Suppose that water from a wetland area is sampled and found to have the given hydronium ion concentration. Determine whether the wetland is a rich fen, a poor fen, or a bog. See Example 3. 2.49*10^-7
Problem 41
- Solve each equation. Give solutions in exact form. See Examples 5–9. ln 4x = 1.5
Problem 43
- In Exercises 43– 48, match the function with its graph from choices A–F. ƒ(x) = log￬2 x
Problem 43
Problem 43a
Solve each problem. Use a calculator to find an approximation for each logarithm. log 398.4
Problem 43c
Solve each problem. Use a calculator to find an approximation for each logarithm. log 3.984
- Solve each equation. Give solutions in exact form. See Examples 5–9. log(2 - x) = 0.5
Problem 45
- Find each value. If applicable, give an approximation to four decimal places. See Example 5. ln e^1.6
Problem 45
- Solve each equation. Give solutions in exact form. See Examples 5–9. log_6 (2x + 4) = 2
Problem 47
- Find each value. If applicable, give an approximation to four decimal places. See Example 5. ln 1/e^2
Problem 47
Problem 48
Graph each function. Give the domain and range. See Example 3. ƒ(x) = 2x+3 +1
- Solve each equation. Give solutions in exact form. See Examples 5–9. log_4 (x^3 + 37) = 3
Problem 49
- Graph each function. Give the domain and range. See Example 3. ƒ(x) = 2^(x+2) - 4
Problem 49