Question

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Chapter 11 part 2:

What are three different properties of logarithmic functions when encountering the operations of addition, subtraction, and multiplication? Provide an example of each.

Answer 1

The three main log rules you'll encounter are

• log(A*B) = log(A) + log(B)
• log(A/B) = log(A) - log(B)
• log(A^B) = B*log(A)

The first rule allows us to go from a log of some product, to a sum of two logs. In short, we go from product to sum. The second rule allows us to go from a quotient to a difference. Lastly, the third rule allows to go from an exponential to a product.

Here are examples of each rule being used (in the exact order they were given earlier).

• log(2*3) = log(2) + log(3)
• log(5/8) = log(5) - log(8)
• log(7^4) = 4*log(7)

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Here's a slightly more complicated example where the log rules are used.

log(x^2y/z)

log(x^2y) - log(z)

log(x^2) + log(y) - log(z)

2*log(x) + log(y) - log(z)

Hopefully you can see which rules are being used for any given step. If not, then let me know and I'll go into more detail.