6. Exponential & Logarithmic Functions

In Exercises 83–88, let logb 2 = A and logb 3 = C and Write each expression in terms of A and C.logb √(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. See Example 8. log_√13 12

Use the change-of-base theorem to find an approximation to four decimal places for each logarithm. See Example 8. 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 (b^4√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 (2x^3) = 3 log4 (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.ln(8x^3) = 3 ln (2x)

Given that log￬10 2 ≈ 0.3010 and log￬10 3 ≈ 0.4771, find each logarithm without using a calculator. log￬10 6

In Exercises 81–100, evaluate or simplify each expression without using a calculator. e^ln 125

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 = x^2

Let u = ln a and v = ln b. Write each expression in terms of u and v without using the ln function. ln √(a^3/b^5)

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)

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 5^2)