6. Exponential & Logarithmic Functions

In Exercises 64–73, solve each exponential equation. Where necessary, express the solution set in terms of natural or common logarithms and use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. $8^x=12143$

Solve each equation. Give solutions in exact form. See Examples 5–9. log x + log(x - 21) = log 100

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+6)+log₃(x+4)=1

Solve each equation. Give solutions in exact form. See Examples 5–9. log(9x + 5) = 3 + log(x + 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+2)−log₂(x−5)=3

Solve each equation. Give solutions in exact form. ln(4x - 2) - ln 4 = -ln(x - 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. 2 log₃(x+4)=log₃ 9 + 2

Solve each equation. Give solutions in exact form. See Examples 5–9. ln(5 + 4x) - ln(3 + x) = ln 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. log₂(x−6)+log₂(x−4)−log₂ x=2

Solve each equation. Give solutions in exact form. See Examples 5–9. . log₅ (x + 2) + log₅ (x - 2) = 1

In Exercises 74–79, solve each logarithmic equation. log2 (x+3) + log2 (x-3) =4

Solve each equation. Give solutions in exact form. See Examples 5–9. log₂ (2x - 3) + log₂ (x + 1) = 1

In Exercises 74–79, solve each logarithmic equation. log₄ (2x+1) = log₄ (x-3) + log₄ (x+5)

Solve each equation. Give solutions in exact form. ln e^x - 2 ln e = ln e⁴

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(3x−3)=log(x+1)+log 4