Logarithmic Equations

What is the definition of a logarithm?

• A logarithm is a mathematical function that describes the relationship between numbers.

• A logarithm is the power to which a number must be raised to obtain another number.

• A logarithm is a type of equation used to solve for unknown variables.

• A logarithm is a method of calculating the area under a curve.

If log_b(x) = y, what is x in terms of b and y?

• x = b^y

• x = y^b

• x = b/y

• x = log_b(y)

What is the power rule for logarithms?

• log_b(m^p) = p * log_b(m) for any positive m and real number p.

• log_b(m^p) = log_b(m) + log_b(p) for any positive m and real number p.

• log_b(m^p) = log_b(m) - p for any positive m and real number p.

• log_b(m^p) = p + log_b(m) for any positive m and real number p.

Solve for x: log_10(x) = 3.

• 100

• 1000

• 10

• 10000

Convert log(x)=y+2 to exponential form.

• 10^(y+2)=x

• x=10^(y-2)

• x=10^(y+3)

• 10^(y)=x+2

What is the change of base formula for logarithms?

• log_b(a) = log_k(a) / log_k(b) for any base k.

• log_b(a) = log_k(b) / log_k(a) for any base k.

• log_b(a) = log_k(a) + log_k(b) for any base k.

• log_b(a) = log_k(a) - log_k(b) for any base k.

Convert 10^(x+5)=100 to logarithmic form.

• log(100)=x+5

• log(10)=x+5

• log(100)=x-5

• log(100)=5-x

Graph the function: f(x) = log_2(x). What is the domain?

• x > 0

• x < 0

• x = 0

• x >= 0

Solve for x: 2^(x-1) = 8.

• x = 2

• x = 3

• x = 4

• x = 5

What is the inverse of the logarithmic function?

• The square root function

• The exponential function

• The polynomial function

• The trigonometric function