Logarithmic Problem Solving

Solve the logarithmic equation: log(x) + log(y) = 4, where x = 10 and y = 100.

• 10000

• 100

• 100000

• 1000

Find the value of x in the equation: log(x) = 3.

• 10

• 1000

• 10000

• 100

Solve the logarithmic equation: log(x) + log(2x) = 2, where x > 0.

• 1

• 10

• 100

• 5

Use logarithms to solve the exponential equation: 2^x = 8.

• 2

• 4

• 6

• 3

Find the domain and range of the logarithmic function: f(x) = log(x + 3).

• Domain: x > -3, Range: x < 3

• Domain: x > -3, Range: All real numbers

• Domain: x > -3, Range: x > 3

• Domain: x > 3, Range: All real numbers

Determine the vertical asymptote of the logarithmic function: f(x) = log(x^2 + 1).

• No vertical asymptote

• x = -1

• x = 1

• x = 0

Condense the logarithmic expression: log(x) + log(y) - log(z).

• log(xy) - log(z)

• log(x) - log(y) + log(z)

• log(x) + log(y) + log(z)

• log(x) + log(yz)

Expand the logarithmic expression: log(x^2) - log(y).

• log(x^2 - y)

• log(x^2/y)

• log(x^2 + y)

• log(x^2 * y)

Solve the logarithmic equation: log(x) + log(2x) = log(3), where x > 0.

• sqrt(3/2)

• x = 4

• x = 2

• x = 1

Use logarithms to solve the exponential equation: 3^(2x) = 27.

• 3/4

• 2/3

• 1/2

• 3/2