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Algebra II — Logarithms and Exponents

Log rules, exponential functions, and key identities

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log_is_friend 15 terms Mar 8, 2026
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Terms 15

1
Logarithm
log_b(x) = y means b^y = x; the exponent needed to get x from base b
2
Natural Log
ln(x) = log base e; inverse of e^x
3
Common Log
log(x) = log base 10
4
Product Rule (logs)
log(ab) = log(a) + log(b)
5
Quotient Rule (logs)
log(a/b) = log(a) − log(b)
6
Power Rule (logs)
log(a^n) = n·log(a)
7
Change of Base Formula
log_b(x) = log(x)/log(b)
8
Exponential Growth
y = a·b^t where b > 1; quantity increases rapidly over time
9
Exponential Decay
y = a·b^t where 0 < b < 1; quantity decreases over time
10
e (Euler's Number)
Approximately 2.718; base of the natural logarithm
11
Half-Life
Time for half of a decaying quantity to remain; t = ln(2)/k
12
Compound Interest
A = P(1 + r/n)^(nt); grows exponentially over time
13
Continuous Growth
A = Pe^(rt); uses base e for continuous compounding
14
Inverse Functions
Logarithms and exponentials are inverse operations
15
Asymptote
Line a function approaches but never reaches; exponentials have horizontal asymptotes