6. Exponential & Logarithmic Functions

For each substance, find the pH from the given hydronium ion concentration to the nearest tenth. See Example 2(a). grapefruit, 6.3*10^-4

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 √(100x)

For each substance, find the pH from the given hydronium ion concentration to the nearest tenth. See Example 2(a). limes, 1.6*10^-2

Use a calculator to find an approximation to four decimal places for each logarithm. ln 144,000

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 ∛(x/y)

For each substance, find the pH from the given hydronium ion concentration to the nearest tenth. See Example 2(a). crackers, 3.9*10^-9

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.logb ((√x y^3)/z^3)

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]