18 flashcards · Shared on 19 August 2026 by AtomAI Library
Flip each card to check yourself.
What does the equation log_b(x) = y mean, where b > 0 and b ≠ 1?
b^y = x
What does the equation log_b(x) = y mean, where b > 0 and b ≠ 1?
b^y = x
What is the domain of the function f(x) = log_b(x), where b > 0 and b ≠ 1?
x > 0
What is the range of an exponential function f(x) = b^x, where b > 0 and b ≠ 1?
y > 0
Which statement describes the relationship between f(x) = b^x and g(x) = log_b(x)?
They are inverse functions
Which logarithm law correctly expands log_b(MN)?
log_b(M) + log_b(N)
How can log_b(M/N) be rewritten?
log_b(M) − log_b(N)
Which expression is equal to log_b(M^k), assuming M > 0?
k log_b(M)
What is log_b(1) for every valid logarithm base b?
0
What is log_b(b) for every valid logarithm base b?
1
Using the change-of-base formula, which expression equals log_b(x)?
ln(x)/ln(b)
Which feature is a horizontal asymptote of the basic exponential graph y = b^x?
y = 0
Which feature is a vertical asymptote of the basic logarithmic graph y = log_b(x)?
x = 0
For which values of b is the function y = b^x increasing?
b > 1
For which values of b is the function y = b^x decreasing?
0 < b < 1
What is the solution of 2^x = 16?
4
What is the solution of log_3(x) = 4?
81
Which model represents exponential growth with initial value A and constant growth rate r per time period?
A(1 + r)^t
Which model represents exponential decay with initial value A and decay rate r, where 0 < r < 1?
A(1 − r)^t