Exponential/Log Review

Front

What is the definition of an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a * b^x, where a is a constant, b is a positive real number, and x is the exponent.

Front

What is the base of a logarithm?

Back

The base of a logarithm is the number that is raised to a power to obtain a given number. For example, in log_b(a) = c, b is the base.

Front

What is the relationship between exponents and logarithms?

Back

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

Front

Solve for p: 4^(p+2) = 64

Back

p = 1

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

If log_2(x + 5) = 3, what is x?

Back

x = 3

Front

What does it mean for a logarithm to be undefined?

Back

A logarithm is undefined for non-positive numbers. For example, log_b(a) is undefined if a <= 0.

Front

Write in exponential form: log_2(1/8) = -3

Back

2^(-3) = 1/8

Front

Solve for x: 3e^x = 63. Round to the nearest hundredth.

Back

x = 3.04

Front

What is the value of log_10(1000)?

Back

log_10(1000) = 3, because 10^3 = 1000.