Understanding Logarithmic Functions

The video tutorial explains how to graph the function y = log base 5 of x by converting it into its exponential form. It discusses the relationship between logarithms and exponents, and how to create a table of values to plot the graph. The tutorial also covers calculating specific x and y values for different powers and graphing the function while considering its domain, which is x > 0.

What does the equation y = log base 5 of x represent?

• y is the power to which 5 must be raised to get x

• x is the power to which y must be raised to get 5

• y is the base that must be raised to 5 to get x

• x is the base that must be raised to y to get 5

Tags

CCSS.HSF-IF.C.7E

When choosing values for graphing, why is it beneficial to select x values that result in simple powers of 5?

• To ensure the graph is a straight line

• To make the graph look more complex

• To make the graphing process faster

• To avoid using a calculator

Tags

CCSS.HSF.BF.B.5

If y = -2, what is the corresponding x value in the function y = log base 5 of x?

• 1/5

• 1/25

• 5

• 25

What is the domain of the function y = log base 5 of x?

• x < 0

• x ≤ 0

• x > 0

• x = 0

Tags

CCSS.HSF-IF.C.7E

Why can't the logarithmic function y = log base 5 of x be defined for x ≤ 0?

• Because 5 raised to any power is always positive

• Because 5 raised to any power cannot be zero or negative

• Because 5 raised to any power is always negative

• Because 5 raised to any power is always zero

Tags

CCSS.HSF-IF.C.7E

What happens to the value of y as x approaches zero in the graph of y = log base 5 of x?

• y approaches positive infinity

• y approaches zero

• y approaches negative infinity

• y remains constant

In the graph of y = log base 5 of x, what is the y-value when x = 5?

• 5

• 2

• 0

• 1

What is the y-value when x = 1 in the graph of y = log base 5 of x?

• 25

• 5

• 1

• 0

Tags

CCSS.HSF-IF.C.7E

How does the graph of y = log base 5 of x behave as x becomes very large?

• It curves upwards and to the right

• It curves downwards and to the left

• It becomes a straight line

• It remains constant

Tags

CCSS.HSF.BF.B.5

What is the y-value when x = 25 in the graph of y = log base 5 of x?

• 4

• 1

• 2

• 3

Tags

CCSS.HSF.BF.B.5