Logarithms and Exponentials Test Review 23-24

Front

What is a logarithm?

Back

A logarithm is the exponent to which a base must be raised to produce a given number. For example, log_b(a) = c means b^c = a.

Front

What is the relationship between logarithms and exponents?

Back

Logarithms are the inverse operations of exponentiation. If b^y = x, then log_b(x) = y.

Front

What is the formula for continuous compound interest?

Back

A = Pe^(rt), where A is the amount of money accumulated after n years, P is the principal amount, r is the annual interest rate, and t is the time in years.

Front

How do you convert from exponential form to logarithmic form?

Back

To convert from exponential form b^y = x to logarithmic form, write it as log_b(x) = y.

Front

What is the product rule of logarithms?

Back

The product rule states that log_b(MN) = log_b(M) + log_b(N).

Front

What is the quotient rule of logarithms?

Back

The quotient rule states that log_b(M/N) = log_b(M) - log_b(N).

Front

What is the power rule of logarithms?

Back

The power rule states that log_b(M^p) = p * log_b(M).

Front

How do you express log(12) + 2log(x) as a single logarithm?

Back

log(12) + 2log(x) = log(12x^2).

Front

What is the formula for exponential decay?

Back

The formula for exponential decay is y = a(1 - r)^t, where a is the initial amount, r is the decay rate, and t is time.

Front

How do you calculate the time it takes for an investment to triple with continuous compounding?

Back

Use the formula t = (ln(3)/r), where r is the interest rate.