Welcome to class!
In today’s class, we will be talking about the theory of logarithms. Enjoy the class!
Rules of logarithms
1) Product Rule:
The logarithm of a product is the sum of the logarithms of the factors.
loga xy = loga x + loga y
2) Quotient Rule:
The logarithm of a quotient is the logarithm of the numerator minus the logarithm of the denominator
loga (x/y) = loga x – loga y
3) Power Rule:
loga xn = nloga x
4) Change of Base Rule:
loga b = logc b / logc a
loga b = 1 / logb a
where x and y are positive, and a > 0, a ≠ 1
Express log 2 4 + log 2 5 as a single logarithm
log 2 4 + log 2 5 = log 2 (4 × 5) = log 2 20
The properties of logarithms
1. loga 1 = 0 since a0 = 1.
2. loga a = 1 since a1 = a.
3. loga ax = x since ax = ax.
Product property: The log of a product equals the sum of the logs.
Quotient Property: The log of a quotient equals the difference of the logs.
Power Property: The log of power equals the product of the power and the log.
- Population growth
- Interest Rate Problems
- Mortgage Problems
- Radioactive Decay Problems
- Earthquake Problems
Laws of Indices:
In our next class, we will be talking about Surds. We hope you enjoyed the class.
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