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Magazine Problem 56
In Exercises \(53-56,\) rewrite the equation in terms of base \(e\). Express the answer in terms of a natural logarithm and then round to three decimal places. $$y=4.5(0.6)^{x}$$
Problem 56
In Exercises \(41-70,\) 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. $$ 3 \ln x-\frac{1}{3} \ln y $$
Problem 56
Solve each logarithmic equation in Exercises \(49-92 .\) Be sure to reject any value of \(x\) that is not in the domain of the original logarithmic expressions. Give the exact answer. Then, where necessary, use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. $$ \log _{2}(x+50)=5 $$
Problem 57
Solve each logarithmic equation in Exercises \(49-92 .\) Be sure to reject any value of \(x\) that is not in the domain of the original logarithmic expressions. Give the exact answer. Then, where necessary, use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. $$ \log _{3}(x+4)=-3 $$
Problem 57
In Exercises \(41-70,\) 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. $$ 3 \ln x-\frac{1}{3} \ln y $$
Problem 57
Begin by graphing \(f(x)=\log _{2} x\). Then use transformations of this graph to graph the given function. What is the vertical asymptote? Use the graphs to determine each function's domain and range. $$ g(x)=\frac{1}{2} \log _{2} x $$
Problem 57
Nigeria has a growth rate of 0.025 or \(2.5 \% .\) Describe what this means.
Problem 58
Solve each logarithmic equation in Exercises \(49-92 .\) Be sure to reject any value of \(x\) that is not in the domain of the original logarithmic expressions. Give the exact answer. Then, where necessary, use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. $$ \log _{7}(x+2)=-2 $$
Problem 58
In Exercises \(41-70,\) 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. $$ 2 \ln x-\frac{1}{2} \ln y $$
Problem 58
How can you tell whether an exponential model describes exponential growth or exponential decay?
