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Logs – Part 2. Review of Logarithms. 3 logarithm shortcuts. 3 logarithm laws. Solving log equations. Solving logarithmic equations takes some instinct, which only comes from practice, but to help you get you started, here is a flowchart with some possibly useful steps.

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review of logarithms
Review of Logarithms

3 logarithm shortcuts

3 logarithm laws

solving log equations
Solving log equations

Solving logarithmic equations takes some instinct, which only comes from practice, but to help you get you started, here is a flowchart with some possibly useful steps.

applications logarithms
Applications - Logarithms

Ex 1. A Sidney Crosby rookie card was purchased in 2005 for $15.00. Its value is set to double every 2 years. When will the card be worth $90.00?

In 5.17 years, the card is worth $90.

applications logarithms1
Applications - Logarithms

Ex 2. A certain radioactive element has a half-life of 8.2 minutes. When will there be 1/10th the original amount?

In this case

y = (1/10)Ao

It will take 27.24 minutes for only 1/10th the original amount to remain.

applications logarithms2
Applications - Logarithms

Ex 3. Sarah bought a computer for $2000. Its value depreciates by 18% every two years.

a. By what percentage does it depreciate every year?

r = 1 – 0.18 = 0.82

This means it will be worth 82% of its value after 2 years.

In one year, it went from being worth $2000 to being worth $1811.08. Dividing tells us that it is 90.554% of $2000, or a depreciation of 9.446% in one year.

applications logarithms3
Applications - Logarithms

Ex 3. Sarah bought a computer for $2000. Its value depreciates by 18% every two years.

b. When is its value $99?

In 30.29 years her computer will be worth $99.