Logarithmic Functions and Scales

The video tutorial explains how to plot values on a log scale, focusing on the properties of a common log scale where each tick mark represents a power of 10. It demonstrates how to determine the position of points A and B, with values 4,000 and 0.002 respectively, by solving exponential equations and converting them into logarithmic form. The tutorial includes step-by-step instructions for using a calculator to approximate logarithms and verify results.

What is the primary characteristic of a logarithmic scale?

• It increases linearly.

• It decreases exponentially.

• It increases by a factor of 10 at each tick mark.

• It remains constant.

To find the position of point A with a value of 4000 on the log scale, which equation do we solve?

• 10^x = 4000

• x^10 = 4000

• 10^4000 = x

• x^4000 = 10

What is the equivalent logarithmic form of the equation 10^x = 4000?

• log base x of 10 = 4000

• log base 10 of 4000 = x

• log base 10 of x = 4000

• log base 4000 of 10 = x

What is the approximate value of x when solving log base 10 of 4000?

• 3.6021

• 4.0000

• 0.0020

• 2.6990

Where should point A be plotted on the log scale?

• Between 10^2 and 10^3

• Between 10^3 and 10^4

• Between 10^1 and 10^2

• Between 10^4 and 10^5

To find the position of point B with a value of 0.002 on the log scale, which equation do we solve?

• x^0.002 = 10

• 10^x = 0.002

• x^10 = 0.002

• 10^0.002 = x

What is the equivalent logarithmic form of the equation 10^x = 0.002?

• log base 10 of x = 0.002

• log base 10 of 0.002 = x

• log base x of 10 = 0.002

• log base 0.002 of 10 = x

What is the approximate value of x when solving log base 10 of 0.002?

• -3.0000

• -2.6990

• -0.0020

• -1.0000

Where should point B be plotted on the log scale?

• Between 10^-1 and 10^-2

• Between 10^-2 and 10^-3

• Between 10^-3 and 10^-4

• Between 10^-4 and 10^-5

What does the common log of a number represent?

• The base of the number

• The square root of the number

• The exponent to which 10 must be raised to get the number

• The number itself