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Guilherme Mazui

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What is the Difference Between log and Natural log?

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The main difference between log and natural log (ln) is the base they are defined for. Log represents a logarithm to the base 10, also known as the common logarithm, while ln represents a logarithm to the base e, also known as the natural logarithm. Here are some key differences between log and ln:

  • Base: Log is defined for base 10, whereas ln is defined for base e.
  • Notation: Log is represented as log10(x), while ln is represented as loge(x) or ln(x).
  • Exponential Form: The exponential form for log is 10x = y, while for ln, it is ex = y.

Logarithms are essential for solving equations where an unknown variable appears as the exponent of a number. They are significant in many branches of mathematics and scientific subjects and are used to solve various problems related to finance, economics, and other fields.

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  • What is the Difference Between log and Natural log?
  • Comparative Table: log vs Natural log

    • Comparative Table: log vs Natural log

    Here is a table summarizing the differences between log (logarithm) and ln (natural logarithm):

    Feature Log (logarithm) Ln (natural logarithm)
    Base Log refers to a logarithm to the base 10 Ln refers to a logarithm to the base e (Euler's number)
    Representation Log is represented as log10(x) Ln is represented as loge(x) or ln(x)
    Exponent Form The exponent form of the common logarithm is 10x = y The exponent form of the natural logarithm is ex = y
    Interrogative "At which number should we raise 10 to get y?" "At which number should we raise e to get y?"

    Logarithms are essential for solving equations where an unknown variable appears as the exponent of a given number. The key difference between log and ln is the base: log is defined for base 10, while ln is denoted for base e, which is an irrational and transcendental number approximately equal to 2.718281828459.

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    Guilherme Mazui

    Guilherme Mazui is graduated in journalism from the Federal University of Minas Gerais (UFMG) and a master's degree in Communication from the University of São Paulo (USP). In addition, he has experience in advertising writing and has worked as a content editor in several companies.