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Magazine Problem 87
In Exercises \(87-90,\) determine whether cach statement is true or false If the statement is false, make the necessary change(s) to produce a true statement. As the number of compounding periods increases on a fixed investment, the amount of money in the account over a fixed interval of time will increase without bound.
Problem 87
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. $$ \log x+\log (x+3)=\log 10 $$
Problem 87
In Exercises \(83-88,\) let \(\log _{b} 2=A\) and \(\log _{b} 3=\) C. Write each expression in terms of \(A\) and \(C\). $$ \log _{b} \sqrt{\frac{2}{27}} $$
Problem 87
Evaluate or simplify each expression without using a calculator. $$ \ln 1 $$
Problem 88
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. $$ \log (x+3)+\log (x-2)=\log 14 $$
Problem 88
Evaluate or simplify each expression without using a calculator. $$ \ln e $$
Problem 89
Evaluate or simplify each expression without using a calculator. $$ \ln e^{6} $$
Problem 89
In Exercises \(89-102,\) determine whether each equation is true or false. Where possible, show work to support your conclusion. If the statement is false, make the necessary change(s) to produce a true statement. $$ \ln e=0 $$
Problem 89
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. $$ \ln (x-4)+\ln (x+1)=\ln (x-8) $$
Problem 90
Evaluate or simplify each expression without using a calculator. $$ \ln e^{7} $$
