6. Exponential & Logarithmic Functions

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

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. log₂ (96) - log₂ (3)

Find each value. If applicable, give an approximation to four decimal places. ln e^1.6

Find each value. If applicable, give an approximation to four decimal places. ln 1/e²

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 x + 3 log y

Find each value. If applicable, give an approximation to four decimal places. ln √e

In Exercises 50–53, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. ${\log }_4\left(\frac{\sqrt{x}}{64}\right)$

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. (1/2)ln x + ln y