logarithm properties Flashcards
What is the Product Rule of logarithms?
logₐ(xy) = logₐ(x) + logₐ(y)
The logarithm of a product is the sum of the logarithms.
What is the Quotient Rule of logarithms?
logₐ(x/y) = logₐ(x) - logₐ(y)
The logarithm of a quotient is the difference of the logarithms.
What is the Power Rule of logarithms?
logₐ(xⁿ) = n * logₐ(x)
The logarithm of a power is the exponent times the logarithm of the base.
What is the Change of Base Formula?
logₐ(x) = logₓ(x) / logₓ(a)
The logarithm of x to base a can be expressed as the ratio of logarithms to any other base.
What is the value of logₐ(1)?
0
The logarithm of 1 to any base is 0.
What is the value of logₐ(a)?
1
The logarithm of the base to itself is 1.
What does a^(logₐx) equal?
x
The exponential and logarithm functions are inverses of each other.
What is ln 1?
ln 1 = 0.
What is ln e?
ln e = 1.
What is the property of ln for multiplication?
ln ab = ln a + ln b.
What is the property of ln for division?
ln a/b = ln a - ln b.
What is the property of ln for exponentiation?
ln am = m ln a.
What is the relationship between e and ln?
eln x = x.
