6. Exponential & Logarithmic Functions

Solve each equation. Give solutions in exact form. See Examples 5–9. 5 ln x = 10

Solve each exponential equation in Exercises 23–48. 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. e^2x−3e^x+2=0

Solve each equation. Give solutions in exact form. See Examples 5–9. ln 4x = 1.5

Solve each exponential equation in Exercises 23–48. 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. e^4x+5e^2x−24=0

Solve each equation. Give solutions in exact form. See Examples 5–9. log(2 - x) = 0.5

Solve each exponential equation in Exercises 23–48. 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. 3^2x+3^x−2=0

Solve each equation. Give solutions in exact form. See Examples 5–9. log_6 (2x + 4) = 2

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. log3 x=4

Solve each equation. Give solutions in exact form. See Examples 5–9. log_4 (x^3 + 37) = 3

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=2

Solve each equation. Give solutions in exact form. See Examples 5–9. ln x + ln x^2 = 3

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. log4(x+5)=3

Solve each equation. Give solutions in exact form. See Examples 5–9. log_3 [(x + 5)(x - 3)] = 2

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. log2(x+25)=4

Solve each equation. Give solutions in exact form. See Examples 5–9. log_2 [(2x + 8)(x + 4)] = 5