Exponents and Logarithms

Front

What is an exponent?

Back

An exponent is a number that indicates how many times to multiply the base by itself. For example, in 2^3, 2 is the base and 3 is the exponent, meaning 2 is multiplied by itself 3 times (2 * 2 * 2 = 8).

Front

What is a logarithm?

Back

A logarithm is the inverse operation to exponentiation, answering the question: to what exponent must a base be raised to produce a given number? For example, log_b(A) = x means b^x = A.

Front

What does the term 'base' refer to in logarithms?

Back

The base in a logarithm is the number that is raised to a power. In log_b(A) = x, b is the base.

Front

How do you convert an exponential equation to a logarithmic equation?

Back

To convert an exponential equation of the form b^x = A to logarithmic form, you write log_b(A) = x.

Front

What is the formula for compound interest?

Back

The formula for compound interest is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the number of years.

Front

What does 'semi-annually' mean in terms of compounding?

Back

Semi-annually means that interest is compounded twice a year.

Front

If a function is given as y = a(1 + r)^t, what do a, r, and t represent?

Back

In the function y = a(1 + r)^t, 'a' is the initial amount, 'r' is the rate of increase (as a decimal), and 't' is the time in years.

Front

What is the value of 10^2?

Back

10^2 = 100.

Front

What is the value of log_10(100)?

Back

log_10(100) = 2, because 10^2 = 100.

Front

What is the relationship between exponents and logarithms?

Back

Exponents and logarithms are inverse operations; if b^x = A, then log_b(A) = x.