Bellwork Find the value of x in each exponential equation.

logarithms and logarithmic functions Section 6.3

Exponentiation: The third power of some number ‘b’ is the product of 3 factors of ‘b’. more generally, raising ‘b’ to the n-th power (n is a natural number) is done by multiplying n factors. The idea of logarithms is to reverse the operation of exponentiation. Definition: If b≠1 and ‘y’ are any two positive real numbers then there exists a unique real number ‘x’ satisfying the equation bx = y. This x is said to be the logarithm of y to the base b and is written as Logb y = x

Two special logarithm values that you should learn to recognize Two special logarithm values that you should learn to recognize. let b be a positive real number such that b ≠ 1.

Types of logarithms: Identities: logarithms to base 10 are called common logarithms logarithms to base 2 are called binary logarithms logarithms to base ‘e’ are called natural logarithms Identities:

A common logarithm is a logarithm with base 10 A common logarithm is a logarithm with base 10. It is denoted by log10 or simply by log. A natural logarithm is a logarithm with base e. It can be denoted by loge but is usually denoted by ln.

Bellwork

In other words, exponential functions and logarithmic functions “undo” each other.

Finding Inverse Functions

You Try