6. Exponential & Logarithmic Functions

Solve each equation. Give solutions in exact form. log₂ (log₂ 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. log x² = (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. p = a + (k/ln x), for x

Solve each equation for the indicated variable. Use logarithms with the appropriate bases. 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. $I=\frac{E}{R}(1-e^{-\frac{Rt}{2}}),\text{ for }t$

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)

Solve each equation for the indicated variable. Use logarithms with the appropriate bases. See Example 10. y = K/(1+ae^-bx), for b

Solve each equation for the indicated variable. Use logarithms with the appropriate bases. y = A + B(1 - e^-Cx), for x

Solve each equation. 5^2x ⋅ 5^4x=125

Solve each equation. 3^x+2 ⋅ 3^x=81