6. Exponential & Logarithmic Functions

In Exercises 71–78, use common logarithms or natural logarithms and a calculator to evaluate to four decimal places. log₁₄ 87.5

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

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 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

In Exercises 89–102, determine whether each equation is true or false. Where possible, show work to support your conclusion. If the statement is false, make the necessary change(s) to produce a true statement. $\left[\frac{log(x+2)}{log(x-1)}\right]=log(x+2)-log(x-1)$

Find each value. If applicable, give an approximation to four decimal places. ln (27 $\times$ 943)

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

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. log(387 $\times$ 23)

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log₆ (36/(√(x+1))

Use the change-of-base theorem to find an approximation to four decimal places for each logarithm. log₂ 5

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 + \(\log\)(x^2 - 1) - \(\log\) 7 - \(\log\)(x + 1)$

Evaluate the given logarithm using the change of base formula and a calculator. Use the natural log. 

$\(\log\)_23789$

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)

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