$$\DeclareMathOperator{cosec}{cosec}$$

# Exponentials and logarithms

Syllabus Content

Know and use the definition of logax as the inverse of ax, where a is positive, not equal to 1 and x ≥ 0.Know and use the function ln x and its graph. Know and use ln x as the inverse function of ex

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## Furthermore

Logarithms are a mathematical concept that provides a way to work with exponential equations in a more linear manner. The logarithm of a number to a given base is the power or exponent to which the base must be raised to produce that number. The most commonly used bases in logarithms are 10, often referred to as the common logarithm, and $$e$$, the base of natural logarithms. The number $$e$$ is an irrational number approximately equal to 2.71828 and has profound significance in mathematics, especially in calculus and complex analysis.

The key formulae for logarithms with base 10 and $$e$$ are:

$$\log_{10}(x) = y \quad \text{means} \quad 10^y = x \\ \log_e(x) = \ln(x) = y \quad \text{means} \quad e^y = x \\ \log_b(m \times n) = \log_b(m) + \log_b(n) \\ \log_b\left(\frac{m}{n}\right) = \log_b(m) - \log_b(n) \\ \log_b(m^n) = n \times \log_b(m)$$

This video on Exponential and Logarithmic Functions is from Revision Village and is aimed at students taking the IB Maths AA SL/HL course

This video on Exponential and Logarithmic Functions is from Revision Village and is aimed at students taking the IB Maths AA Standard level course.

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