6. Exponential & Logarithmic Functions

For each substance, find the pH from the given hydronium ion concentration to the nearest tenth. grapefruit, 6.3$\times$10^-4

If log 3 = A and log 7 = B, find log7 (9) in terms of A and B.

Use the various properties of exponential and logarithmic functions to evaluate the expressions in parts (a)–(c). Given g(x) = e^x, find g(ln ln 5²)

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(8x³) = 3 ln (2x)

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. $\(\frac{1}{3}\) \(\left\)[ 2 \(\ln\)(x + 5) - \(\ln\) x - \(\ln\) (x^2 - 4) \(\right\)]$

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. ln(e²/5)

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

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. (1/2)(log x + log y)

Answer each of the following. Between what two consecutive integers must log₂ 12 lie?

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(5x) + ln 1 = ln(5x)

Find each value. If applicable, give an approximation to four decimal places. log 387 + log 23

Find each value. If applicable, give an approximation to four decimal places. log 63

In Exercises 58–59, use common logarithms or natural logarithms and a calculator to evaluate to four decimal places. log₄ 0.863

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log₇ (7/x)