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. (1/2)^x = 5

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. 0.8^x = 4

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. log₃ [(x + 5)(x - 3)] = 2

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(2)^x-2 + 1 = 100

Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents. 2^x=64

Use the properties of inverses to determine whether ƒ and g are inverses. ƒ(x) = log￬2 x+1, g(x) = 2^x-1

Solve each equation. 2|ln x|−6=0

Graph f(x) = 2^x and g(x) = log2 x in the same rectangular coordinate system. Use the graphs to determine each function's domain and range.

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

Solve the exponential equation.

$2\(\cdot\)10^{3x}=5000$

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. $8^x=12143$

Exercises 137–139 will help you prepare for the material covered in the next section. Solve: x(x - 7) = 3.

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^(5x−3) - 2 =10,476

Exercises 137–139 will help you prepare for the material covered in the next section. Solve: (x + 2)/(4x + 3) = 1/x