Law of Logs
This law says when you multiply inside a log, you add the logs.
What is the product rule?
log(50) + log(200)
What is log(10,000) = 4?
log₃(5x²)
What is log₃5 + 2log₃x?
log x + log y
What is log(xy)?
Write log₂3 using natural logs.
What is ln(3)/ln(2)?
This law says when you divide inside a log, you subtract the logs.
What is the Quotient Rule?
log₄(960) − log₄(60)
What is log₄(16) = 2?
ln(2xy)
What is ln2 + lnx + lny?
log x − log y
What is log(x/y)?
Write log₁₅(4784) using common logs.
What is log(4784)/log(15)?
This law allows you to bring an exponent in front of a log.
What is the Power Rule?
log₂(8³⁵)
What is 35·log₂(8) = 35·3 = 105?
log₅( (5x²)/√y )
What is log₅5 + 2log₅x − (1/2)log₅y?
3log₂5 + (1/2)log₂7
What is log₂(5³√7)?
Why do we use change of base?
What is because calculators only compute log (base 10) and ln (base e)?
This is the base used in natural logarithms (ln).
What is e?
log₂6 − log₂15 + log₂20
What is log₂( (6·20)/15 ) = log₂(8) = 3?
log(√ab)
What is (1/2)(log a + log b)?
logb(x2-1)-logb(x-1)
What is logb(x + 1)?
In Ebbinghaus’ Law, what does “t” represent?
What is time in months?
This rule converts logs from one base to another using division.
What is the Change-of-Base Formula?
log₅(25)
What is 2?
log(x³y²/z)
What is 3logx + 2logy − logz?
log x + log(x² − 49) − log 5 − log(x + 9)
What is log( (x(x−7)) / 5 )?
If log(P) = log(87) − 0.3log(25), solve conceptually: does P increase or decrease over time?
What is decrease?