Logarithms and Exponential Problems

Front

What is the product rule of logarithms?

Back

log_b(xy) = log_b(x) + log_b(y)

Front

What is the power rule of logarithms?

Back

log_b(x^n) = n * log_b(x)

Front

What is the quotient rule of logarithms?

Back

log_b(x/y) = log_b(x) - log_b(y)

Front

What is the change of base formula for logarithms?

Back

log_b(a) = log_k(a) / log_k(b) for any base k.

Front

What is the definition of a logarithm?

Back

A logarithm is the exponent to which a base must be raised to produce a given number.

Front

What is the relationship between logarithms and exponentials?

Back

Logarithms and exponentials are inverse functions.

Front

If log_b(x) = y, what is the equivalent exponential form?

Back

b^y = x

Front

What is the value of log_10(1000)?

Back

3, because 10^3 = 1000.

Front

What is the value of log_2(8)?

Back

3, because 2^3 = 8.

Front

What is the formula for compound interest?

Back

A = P(1 + r/n)^(nt), where A is the amount, P is the principal, r is the rate, n is the number of times interest is compounded per year, and t is the time in years.