Ch 3 Test Review

y=2^x

x = log_2(y)

Vertical stretch by 3, Right 5 units, Up 2

x = \frac{\ln 13 - 4}{3}

Horizontal shift left 5 units

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

The base of a logarithm is the number that is raised to a power to obtain a certain value.

log_b(a) = \frac{log_k(a)}{log_k(b)} for any base k.

A vertical stretch multiplies the output of the function by a factor greater than 1, making the graph taller.

A horizontal shift moves the graph left or right along the x-axis.