6. Exponential & Logarithmic Functions

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)

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^{log_2 2})

Find each value. If applicable, give an approximation to four decimal places. log 10¹²

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. 3 ln x + 5 ln y - 6 ln z

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.

$lo{g}_b(x^3+y^3)=3lo{g}_{b}x+3lo{g}_{b}y$

Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places. log_π 63

In Exercises 50–53, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. $\ln \sqrt[3]{\frac{x}{e}}$

Use the various properties of exponential and logarithmic functions to evaluate the expressions in parts (a)–(c). Given ƒ(x) = log₂ x, find ƒ(2⁷)

Use the various properties of exponential and logarithmic functions to evaluate the expressions in parts (a)–(c). Given ƒ(x) = 3^x, find ƒ(log₃ (ln 3))

Find each value. If applicable, give an approximation to four decimal places. ln 98 - ln 13

Solve: log₂ (x+9) — log₂ x = 1.

Use properties of logarithms to rewrite each function, then graph. ƒ(x) = log₃ [9 (x+2) ]

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log₄ (64/y)

Find each value. If applicable, give an approximation to four decimal places. log 0.1

Use the various properties of exponential and logarithmic functions to evaluate the expressions in parts (a)–(c). Given ƒ(x) = 3^x, find ƒ(log₃ (2 ln 3))