91Ó°ÊÓ

Evaluate each expression without using a calculator. $$\log _{5} 5^{7}$$

Use properties of logarithms to expand logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. \(\log \left[\frac{10 x^{2} \sqrt[3]{1-x}}{7(x+1)^{2}}\right]\)

Evaluate each expression without using a calculator. $$\log _{4} 4^{6}$$

Use properties of logarithms to expand logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. \(\log \left[\frac{100 x^{3} \sqrt[3]{5-x}}{3(x+7)^{2}}\right]\)

Solve each exponential equation. Express the solution set in terms of natural logarithms or common logarithms. Then use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. $$3^{\frac{x}{7}}=0.2$$

Solve each exponential equation. Express the solution set in terms of natural logarithms or common logarithms. Then use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. $$5^{2 x+3}=3^{x-1}$$

Evaluate each expression without using a calculator. $$8^{\log _{8} 19}$$

Use properties of logarithms to condense logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator. \(\log 5+\log 2\)

Solve each exponential equation. Express the solution set in terms of natural logarithms or common logarithms. Then use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. $$7^{2 x+1}=3^{x+2}$$

Use properties of logarithms to condense logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator. \(\log 250+\log 4\)