6. Exponential & Logarithmic Functions

In Exercises 83–88, let log_b 2 = A and log_b 3 = C and Write each expression in terms of A and C.

log_b (3/2)

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

In Exercises 83–88, let log_b 2 = A and log_b 3 = C and Write each expression in terms of A and C.

log_b 8

Let log_b 2 = A and log_b 3 = C and Write each expression in terms of A and C. log_b √(2/27)

Solve: log₂ (x+9) — log₂ x = 1.

Use the change-of-base theorem to find an approximation to four decimal places for each logarithm. log_√13 12

Use the change-of-base theorem to find an approximation to four decimal places for each logarithm. log_√19 5

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)

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. log₄ (2x³) = 3 log₄ (2x)

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)

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.

x log 10^x = x²

Let u = ln a and v = ln b. Write each expression in terms of u and v without using the ln function. ln √(a³/b⁵)

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

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 1/e)

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)