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Log rules

13 formulas · what each one means · a free lesson for each

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Log rules

Definition
logb x = y ⇔ by = x
A log is a power: the power of b that gives x.Lesson: Exponential equations and logarithms →
Product rule
logb(MN) = logb M + logb N
Times inside → plus outside.Lesson: Log properties with letters →
Quotient rule
logb MN = logb M − logb N
Divide inside → minus outside.Lesson: Log properties with letters →
Power rule
logb(Mp) = p logb M
The power comes down in front.Lesson: Log properties with letters →
Change of base
logb x = log xlog b = ln xln b
How a calculator finds any log.Lesson: Exponential equations and logarithms →
Special values
logb b = 1 logb 1 = 0 blogb x = x
Lesson: Exponential equations and logarithms →
Natural log
ln x = loge x, e ≈ 2.718
Lesson: Natural logarithms →
Log equations
check every answer: no log of 0 or a negative
Some answers are false and must be thrown away.Lesson: Log equations with false answers →

Interest and growth

Compound interest
A = P(1 + rn)nt
n = times a year it is added (monthly: 12), t = years.Lesson: Compound and continuous interest →
Continuous interest
A = Pert
Lesson: Compound and continuous interest →
Half-life
A = A0 (12)t/h
h is the half-life: the time for half to go.Lesson: Half-life and time with logs →
Savings plan (future value)
FV = PMT × (1 + i)N − 1i
i = rate per payment, N = number of payments.Lesson: Savings plans →
Loan payment
PMT = P × i1 − (1 + i)−N
Rounded up to the next cent.Lesson: Loan payments →

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