Basics Flashcards
What is a logarithm?
A logarithm answers the question: ‘To what power must I raise the base to get this number?’
What is the general form of a logarithm?
log_b(x) = y means b^y = x
What is the log base 10 called?
The common logarithm, written as log(x)
What is the log base e called?
The natural logarithm, written as ln(x)
What is the number e approximately equal to?
e ‚ 2.718… ‚ an irrational number that appears in continuous growth
What is ln(e)?
ln(e) = 1
What is ln(1)?
ln(1) = 0
What is the inverse relationship of natural logs?
ln(e^x) = x and e^(ln(x)) = x
What is the product rule for logarithms?
log_b(x * y) = log_b(x) + log_b(y)
What is the quotient rule for logarithms?
log_b(x / y) = log_b(x) - log_b(y)
What is the power rule for logarithms?
log_b(x^r) = r * log_b(x)
What is the change of base formula?
log_b(x) = log_k(x) / log_k(b) ‚often with base 10 or e
Why are logs useful in real life?
They help solve exponential problems, like time in growth or sound intensity.
What does ln compress?
Large numbers‚ ln grows slowly, turning big numbers into manageable ones
