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(1000x)

Find each value. If applicable, give an approximation to four decimal places. log 518 - log 342

Use properties of logarithms to rewrite each function, then graph. ƒ(x) = log₂ [4 (x-3) ]

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. 4 ln (x + 6) - 3 ln x

Let u = ln a and v = ln b. Write each expression in terms of u and v without using the ln function. ln (b⁴ √a)

Work each problem. Which of the following is equivalent to ln(4x) - ln(2x) for x > 0? A. 2 ln x B. ln 2x C. (ln 4x)/(ln 2x) D. ln 2

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log_b ((x²y)/z²)

In Exercises 125–128, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.

$\frac{lo{g}_{7}49}{lo{g}_{7}7}=lo{g}_{7}49-lo{g}_{7}7$

Expand: $lo{g}_8\left(\frac{4\surd x}{64y3}\right)$

Find each value. If applicable, give an approximation to four decimal places. ln 0.00013

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log N^-6

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

$\(\log\)_317$

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. 2 log_b x + 3 log_b y

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. ln(x + 1) = ln x + ln 1