6. Exponential & Logarithmic Functions

Solve each equation. In Exercises 11–34, give irrational solutions as decimals correct to the nearest thousandth. In Exercises 35-40, give solutions in exact form. 2e^2x + e^x = 6

Solve each equation. Give solutions in exact form. log(2 - x) = 0.5

Solve each equation. 3|log x|−6=0

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. Give solutions in exact form. ln(4x - 2) - ln 4 = -ln(x - 2)

n Exercises 92–93, rewrite the equation in terms of base e. Express the answer in terms of a natural logarithm and then round to three decimal places. y = 6.5(0.43)^x

Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents. 6^(x−3)/4=√6

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 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^x=5.7

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. 3e^5x=1977

Solve each equation for the indicated variable. Use logarithms with the appropriate bases. log A = log B - C log x, for A

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. 10^x = 7000

Use the properties of inverses to determine whether ƒ and g are inverses. ƒ(x) = log￬4 (x+3), g(x) = 4^x + 3

Solve each equation. In Exercises 11–34, give irrational solutions as decimals correct to the nearest thousandth. In Exercises 35-40, give solutions in exact form. 3^x = 7

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