Understanding Logarithmic Functions

The video tutorial covers the logarithmic function f(x) = log base 5 of x, exploring its properties and characteristics. It begins with graphing the function and converting it to exponential form. The domain and range are analyzed, followed by finding intercepts and asymptotes. The behavior of the function is discussed, including increasing and decreasing rates. Inequalities are solved to determine when the function is positive or negative. Finally, specific values of the function are calculated and verified using the graph.

What is the exponential form of the function f(x) = log base 5 of x?

• 5^y = x

• y^5 = x

• x^5 = y

• 5^x = y

What is the domain of the function f(x) = log base 5 of x?

• x > 0

• x <= 0

• x < 0

• x >= 0

What is the range of the function f(x) = log base 5 of x?

• x >= 0

• All real numbers

• x > 0

• x < 0

Where does the function f(x) = log base 5 of x intersect the x-axis?

• (5, 0)

• (0, 5)

• (1, 0)

• (0, 1)

What is the vertical asymptote of the function f(x) = log base 5 of x?

• y = 0

• y = 1

• x = 0

• x = 1

Does the function f(x) = log base 5 of x have a y-intercept?

• Yes, at y = 1

• No, it does not exist

• Yes, at y = 5

• Yes, at y = 0

How does the function f(x) = log base 5 of x behave as x increases?

• It remains constant

• It decreases

• It increases at an increasing rate

• It increases at a decreasing rate

For which values of x is the function f(x) = log base 5 of x positive?

• x < 1

• x = 1

• x < 0

• x > 1

For which values of x is the function f(x) = log base 5 of x negative?

• x < 1

• x > 1

• x = 0

• 0 < x < 1

What is the value of x when f(x) = 1 for the function f(x) = log base 5 of x?

• x = 10

• x = 0

• x = 5

• x = 1