91Ó°ÊÓ

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

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. $$7^{0.3 x}=813$$

We see from the calculator screen at the bottom of the previous page that a logistic growth model for world population, \(f(x),\) in billions, \(x\) years after 1949 is $$ f(x)=\frac{12.57}{1+4.11 e^{-0.026 x}} $$ How well does the function model the data showing a world population of 6.9 billion for \(2010 ?\)

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

evaluate each expression $$\log _{4} 4^{6}$$

We see from the calculator screen at the bottom of the previous page that a logistic growth model for world population, \(f(x),\) in billions, \(x\) years after 1949 is $$ f(x)=\frac{12.57}{1+4.11 e^{-0.026 x}} $$ When did world population reach 7 billion?

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. $$3^{\frac{x}{7}}=0.2$$

We see from the calculator screen at the bottom of the previous page that a logistic growth model for world population, \(f(x),\) in billions, \(x\) years after 1949 is $$ f(x)=\frac{12.57}{1+4.11 e^{-0.026 x}} $$ When will world population reach 8 billion?

evaluate each expression $$8^{\log _{8} 19}$$

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. $$5^{2 x+3}=3^{x-1}$$