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## Logarithmic Functions

#### High School Functions - HSF-LE.A.4

What Are Logarithmic Functions? Much before calculus, mathematicians used logarithmic functions to help them with complicated math problems. Like calculus, logarithmic functions helped mathematicians in converting multiplication problems into addition and subtraction problems. Even today, scientists and mathematicians have to encounter problems with large powers and complicated multiplications. This is where logarithmic functions are helpful. DEFINITION OF LOGARITHMIC FUNCTION - In mathematics, the logarithmic function is defined as the inverse of the exponential function. Any exponential function can be easily expressed as the logarithmic function. Similarly, a logarithmic function can be expressed as an exponential form. The logarithmic function allows us to work with large numbers, especially those with large powers. A logarithmic function is expressed as: For x > 0, a > 0, and a ≠ 1 y = logax if and only if x = ay Then the function is shown as f(x)= loga x ‘a’ is the base of the logarithmic function. This is usually read as the log of base a of x. Logarithmic function commonly has two types of bases, which are base e and base 10. The logarithmic function that has base 10 is known as the common logarithmic function. It is denoted by log10 or is simply known as log f(x)= log10 x The logarithmic function that has a base ‘e’ is termed as the natural logarithmic function. It is denoted by loge f(x)= loge x These worksheets will help students read and interpret logarithmic functions in a wide array of situations.