6. Exponential & Logarithmic Functions

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} \(\right\))$

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

Use the various properties of exponential and logarithmic functions to evaluate the expressions in parts (a)–(c). Given ƒ(x) = log₂ x, find ƒ(2^{2 log_2 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^-5

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

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

For each substance, find the pH from the given hydronium ion concentration to the nearest tenth. limes, 1.6$\times$10^-2

Find each value. If applicable, give an approximation to four decimal places. log 0.0022

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. $\(\frac{1}{2}\) \(\left\)( \(\log\)_5 x + \(\log\)_5 y \(\right\)) - 2 \(\log\)_5 (x + 1)$

Find each value. If applicable, give an approximation to four decimal places. ln 27 + ln 943

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} \(\right\))$

Write the log expression as a single log.

$\(\ln\]\frac{3x}{y}\)+2\(\ln\)2y-\(\ln\)4x$

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. 5 ln x - 2 ln y

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. $\(\log\)_6 \(\left\)( \(\frac{x - 1}{x^2 + 4}\) \(\right\)) = \(\log\)_6 (x - 1) - \(\log\)_6 (x^2 + 4)$

Use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. (1/2)ln x - ln y