6. Exponential & Logarithmic Functions

For each substance, find the pH from the given hydronium ion concentration to the nearest tenth. crackers, 3.9$\times$10^-9

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. ${\log }_b\left(\frac{\sqrt{x}{y}^3}{z^3}\right)$

Find the [H₃O⁺] for each substance with the given pH. Write answers in scientific notation to the nearest tenth. soda pop, 2.7

Use a calculator to find an approximation to four decimal places for each logarithm. log_2/3 5/8

Find the [H₃O⁺] for each substance with the given pH. Write answers in scientific notation to the nearest tenth. beer, 4.8

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. $\log_5 \sqrt[3]{\frac{x^2 y}{24}}$

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. $\ln \left( \frac{x^3 \sqrt{x^2 + 1}}{(x + 1)^4} \right)$

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. 2.49$\times$10^-5

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. $\log \left( \frac{10x^2 \sqrt[3]{1 - x}}{7(x + 1)^2} \right)$

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. 2.49$\times$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. 2.49$\times$10^-7

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

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

Solve each problem. Use a calculator to find an approximation for each logarithm. log 3.984