Glossary

The formula for continuous compound interest, $A = Pe^{rt}$, uses base e to represent the exponential growth of money over time.

To calculate $\log_4(64)$ using a calculator that only has $\ln$ or $\log$, you can apply the Change of Base Property to get $\frac{\ln(64)}{\ln(4)}$.

For the function $f(x) = \log(x+5)$, the domain requires that $x+5 > 0$, meaning $x > -5$.

The graph of $y = -3\log(x-1) + 2$ demonstrates graphical transformations including a reflection, vertical stretch, horizontal shift right, and vertical shift up from the parent function $y = \log(x)$.

Since $10^2 = 100$, the inverse relationship means $\log_{10}(100) = 2$, effectively reversing the exponential operation.

If you're trying to find out how many years it takes for an investment to double with continuous compounding, a logarithmic function like $\ln(2)$ will help you solve for time.

In modeling continuous growth, such as bacterial population, you might use the natural logarithm to find the time it takes to reach a certain population size.

When solving for 't' in an equation like $\log(1.03^t) = \log(5)$, the Power Property allows you to bring 't' down as a multiplier: $t \log(1.03) = \log(5)$.

To expand $\log_5(25x)$, you can use the Product Property to write it as $\log_5(25) + \log_5(x) = 2 + \log_5(x)$.

No matter how large or small the positive input to $y = \log_b(x)$, the output can span from negative to positive infinity, illustrating its range is $(-\infty, \infty)$.