Exponent and logarithm rules flashcards

Question 1

State the product rule for exponents with the same base.

Accepted Answer

$$b^m\cdot b^n=b^{m+n}$$ for $b
eq 0$ (typically $b>0$ in algebra).

Question 2

State the product rule for logarithms.

Accepted Answer

$$\log_b(MN)=\log_b(M)+\log_b(N)$$ for $M>0$ and $N>0$.

Question 3

When do you use $A(t)=A_0e^{kt}$ for growth/decay, and what do $A_0$ and $k$ mean?

Accepted Answer

Use it for continuous exponential growth/decay. $A_0$ is the initial amount at $t=0$, and $k$ is the continuous rate ($k>0$ growth, $k<0$ decay); $e$ is the base of the natural log $\ln(x)=\log_e(x)$.

Exponent and logarithm rules flashcards

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