Master logarithmic functions, understand properties, learn change of base, and apply logarithms to solve real-world problems.
Calculate the value of the logarithm!
Expression:
Apply logarithm properties to expand or simplify!
Property: Product Rule
Result:
A logarithmic function is the inverse of an exponential function. If y = bˣ, then x = log_b(y). The logarithmic function has the form f(x) = log_b(x), where b > 0, b ≠ 1 is the base.
f(x) = log₂(x)
• Base: 2
• Domain: (0, ∞) - only positive numbers
• f(1) = log₂(1) = 0 (since 2⁰ = 1)
• f(2) = log₂(2) = 1 (since 2¹ = 2)
• f(8) = log₂(8) = 3 (since 2³ = 8)
If 2³ = 8, then log₂(8) = 3
• The logarithm answers: "2 to what power equals 8?"
• Answer: 3, because 2³ = 8
• Logarithms and exponentials are inverse functions