6. Exponential & Logarithmic Functions

Solve each equation. Give solutions in exact form. See Examples 5–9. log_2 (2x - 3) + log_2 (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. See Examples 5–9. ln e^x - 2 ln e = ln e^4

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

Solve each equation. Give solutions in exact form. See Examples 5–9. log_2 (log_2 x) = 1

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 log x=log 25

Solve each equation. Give solutions in exact form. See Examples 5–9. log x^2 = (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. log(x+4)−log 2=log(5x+1)

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 log x−log 7=log 112

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

Solve each equation for the indicated variable. Use logarithms with the appropriate bases. See Example 10. p = a + (k/ln x), for x

Solve each equation for the indicated variable. Use logarithms with the appropriate bases. See Example 10. r = p - k ln t, for t

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)

Solve each equation for the indicated variable. Use logarithms with the appropriate bases. See Example 10. I = E/R (1- e^(-(Rt)/2), for t

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)−ln(x+3)=ln(x−1)−ln(x+7)