6. Exponential & Logarithmic Functions

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)

Write the single logarithm as a sum or difference of logs.

$\(\log\)_3\(\left\)(\(\frac{\sqrt{x}\)}{9y^2}\(\right\))$

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 4)

Use a graphing utility and the change-of-base property to graph each function. y = log₃ x

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 - (1/3) ln y

Use a graphing utility and the change-of-base property to graph each function. y = log₂ (x + 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 x³

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log √(100x)

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. $\(\log\)_5 \(\sqrt\)[3]{\(\frac{x^2 y}{24}\)}$

Retaining the Concepts. Expand: ${\log }_7\left(\frac{5\sqrt{x}}{49y^{10}}\right)$

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log_b (x² y)

Find each value. If applicable, give an approximation to four decimal places. ln 28

Write the single logarithm as a sum or difference of logs.

$\(\log\)_5\(\left\)(\(\frac{5\left(2x+3\right)^2}{x^3}\]\right\))$

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

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. log x + 3 log y