Logarithmic and Exponential Review

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. For example, if b^y = x, then log_b(x) = y.

Front

What is the relationship between logarithms and exponents?

Back

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

Front

What is the change of base formula for logarithms?

Back

log_b(a) = log_k(a) / log_k(b), where k is any positive number.

Front

Evaluate: log_3(81)

Back

4, because 3^4 = 81.

Front

What is the value of x in the equation 10^x = 20?

Back

x = log_10(20) ≈ 1.301.

Front

Solve for x: 9^(8-x) = 27^(x-3)

Back

x = 5.

Front

What is an asymptote in the context of exponential functions?

Back

An asymptote is a line that a graph approaches but never touches. For f(x) = 2^(x-1) + 3, the horizontal asymptote is y = 3.

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 variable.

Front

Solve for x: log_6(3x - 2) = log_6(5x - 8)

Back

x = 3.

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 certain value. For example, in log_b(a), b is the base.