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Magazine Problem 21
Solve each exponential equation by expressing each side as a power of the same base and then equating exponents. $$e^{x+1}=\frac{1}{e}$$
Problem 22
Solve each exponential equation by expressing each side as a power of the same base and then equating exponents. $$e^{x+4}=\frac{1}{e^{2 x}}$$
Problem 22
evaluate each expression $$\log _{7} 49$$
Problem 22
Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible,evaluate logarithmic expressions without using a calculator. $$\log _{b}\left(x y^{3}\right)$$
Problem 23
Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible,evaluate logarithmic expressions without using a calculator. $$\log _{4}\left(\frac{\sqrt{x}}{64}\right)$$
Problem 23
evaluate each expression $$\log _{2} 64$$
Problem 23
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. $$10^{x}=3.91$$
Problem 24
Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible,evaluate logarithmic expressions without using a calculator. $$\log _{5}\left(\frac{\sqrt{x}}{25}\right)$$
Problem 24
evaluate each expression $$\log _{3} 27$$
Problem 24
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. $$10^{x}=8.07$$
