What is the product property of logarithms?
$\log_b(xy) = \log_b(x) + \log_b(y)$
What is the power property of logarithms?
$\log_b(x^n) = n\log_b(x)$
What is the change of base formula for logarithms?
$\log_b(x) = \frac{\log_a(x)}{\log_a(b)}$
How to express natural log in base e?
$\ln(x) = \log_e(x)$
What is a logarithm?
The inverse function to exponentiation. If $b^y = x$, then $\log_b(x) = y$.
What is the natural logarithm?
The logarithm with base *e*, denoted as $\ln(x)$.
What is the base of the natural logarithm?
The mathematical constant *e*, approximately equal to 2.71828.
Explain the product property of logarithms.
The logarithm of a product is equal to the sum of the logarithms of the individual factors.
Explain the power property of logarithms.
The logarithm of a number raised to a power is equal to the power multiplied by the logarithm of the number.
Explain the change of base property of logarithms.
Allows you to convert a logarithm from one base to another, useful when calculators don't have the desired base.
Explain the relationship between logarithmic and exponential functions.
Logarithmic functions are the inverses of exponential functions. They 'undo' each other.
