Quiz on Logarithms

Solve the real-world problem using logarithms: If a car depreciates at a rate of 20% per year, how many years will it take for the car's value to be half of its original value?

• Approximately 3 years

• Approximately 4 years

• Approximately 5 years

• Approximately 6 years

Solve the logarithmic equation: \log_2(x) + \log_2(x-2) = 3

Solve the logarithmic equation: \log(x-1) = 2

Convert the logarithmic form to exponential form: \log_5(125) = 3

Solve the real-world problem using logarithms: If the intensity of an earthquake is measured to be 1000 times the minimum intensity, what is its magnitude on the Richter scale?

• 3

• 4

• 5

• 6

Solve the logarithmic equation: \log_5(x) + \log_5(2x-1) = 2

• The graph is a curve that passes through (1,0) and becomes steeper as x increases.

• The graph is a straight line passing through the origin.

• The graph is a parabola opening upwards.

• The graph is a hyperbola.

Solve the real-world problem using logarithms: A certain radioactive substance decays at a rate of 5% per year. If you start with 100 grams, how much will remain after 20 years?

• Approximately 35.85 grams

• Approximately 50 grams

• Approximately 60 grams

• Approximately 75 grams

Convert the logarithmic form to exponential form: \log_7(49) = 2