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.
