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Magazine Problem 5
Find the solution of the exponential equation, correct to four decimal places. $$2^{1-x}=3$$
Problem 5
Express the equation in exponential form. (a) \(\log _{8} 2=\frac{1}{3}\) (b) \(\log _{2}\left(\frac{1}{8}\right)=-3\)
Problem 5
Evaluate the expression. $$\log _{4} 192-\log _{4} 3$$
Problem 5
These exercises use the population growth model. The population of a certain city was 112,000 in 1998 and the observed relative growth rate is 4% per year. (a) Find a function that models the population after t years. (b) Find the projected population in the year 2004. (c) In what year will the population reach 200,000?
Problem 5
Sketch the graph of the function by making a table of values. Use a calculator if necessary. $$f(x)=2^{x}$$
Problem 6
Evaluate the expression. $$\log _{12} 9+\log _{12} 16$$
Problem 6
Find the solution of the exponential equation, correct to four decimal places. $$3^{2 x-1}=5$$
Problem 6
Express the equation in exponential form. (a) \(\log _{3} 81=4\) (b) \(\log _{8} 4=\frac{2}{3}\)
Problem 6
These exercises use the population growth model. The frog population in a small pond grows exponentially. The current population is 85 frogs, and the relative growth rate is 18% per year. (a) Find a function that models the population after \(t\) years. (b) Find the projected population after 3 years. (c) Find the number of years required for the frog population to reach 600.
Problem 6
Sketch the graph of the function by making a table of values. Use a calculator if necessary. $$g(x)=8^{x}$$
