6. Exponential & Logarithmic Functions

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

Use a calculator to find an approximation to four decimal places for each logarithm. log₂/₃ 5/8

In Exercises 21–42, evaluate each expression without using a calculator. log5 5

Solve each equation. log￬9 x = 5/2

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

In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.log5 ∛((x^2 y)/24)

In Exercises 36–38, begin by graphing f(x) = log2 x Then use transformations of this graph to graph the given function. What is the graph's x-intercept? What is the vertical asymptote? Use the graphs to determine each function's domain and range. g(x) = log2 (x-2)

In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.ln[(x^3(√(x^2 + 1))/(x + 1)^4]

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

In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.log [(10x^2∛(1 - x))/(7(x + 1)^2)]

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

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

In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator.log 5 + log 2

Solve each problem. Use a calculator to find an approximation for each logarithm. log 398.4

In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator.ln x + ln 7