Unit 2B Log and Exponential Review EXTRA PRACTICE

Front

Change to Exponential Form: log_6(36) = 2

Back

6^2 = 36

Front

Solve for x: ln(x - 2) = 3

Back

x = e^3 + 2

Front

Let h(x) = ln(x) and k(x) = ln(x/2). What is the relationship between the graphs of h and k?

Back

The graph of h is a horizontal dilation of the graph of k by a factor of 1/2.

Front

Consider the functions h(x) = 3^x and k(x) = 9^(x - 1). What is the x-coordinate of the point of intersection of the graphs of h and k?

Back

2

Front

Find the x-coordinates of the points of intersection of f(x) = log_{10}(x + 3) + log_{10}(x - 5) and g(x) = log_{10}(3x - 1).

Back

7 only

Front

Definition: Logarithm

Back

The logarithm is the inverse operation to exponentiation, answering the question: to what exponent must a base be raised, to produce a given number.

Front

Definition: Natural Logarithm (ln)

Back

The natural logarithm is the logarithm to the base e, where e is approximately equal to 2.71828.

Front

Definition: 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 the base, and x is the exponent.

Front

Property: log_b(mn)

Back

log_b(mn) = log_b(m) + log_b(n) (Product Property of Logarithms).

Front

Property: log_b(m/n)

Back

log_b(m/n) = log_b(m) - log_b(n) (Quotient Property of Logarithms).