Logarithm
Logarithm is a mathematical operation that is the inverse of the exponent or reappointment.
The basic formula of logarithms:
bc = a blog written as a = c (b is called the base)
Some people write blogs as logba a = c = c.Table of contents

    1 Basis
    2 Notation
    3 Finding logarithm
    4 Formulas
    5 The use of logarithms
        5.1 Science and engineering
        5.2 Calculation of the easier
        5.3 Calculus
    6 Calculation of the value of the logarithm
    7 See also
Base
The base is often used or most widely used is the base 10, e ≈ 2.71828 ... and 2.Notation

    In Indonesia, most math textbooks use a blog rather than logba notation. Math books in English using the notation logba
    Some people write ln a elog instead of a, a log instead of a 10Log a and ld instead 2log a.
    On most calculators, the LOG refers to logarithm base 10, and LN refer to e-based logarithm.
    In some computer programming languages ​​such as C, C + +, Java and BASIC, LOG refers to e-based logarithm.
    Sometimes log x (uppercase L) refers to 10Log x and log x (lowercase L) points to elog x.
Looking logarithm
How to find the value of logarithms include using:

    Table
    Calculator (which has features log)
FormulaLogarithmac = b → ª log b = ca = baseb = numbers dilogaritmac = logarithm resultsProperties of Logarithmsª log a = 1ª log 1 = 0log ª a ⁿ = nª ⁿ log b = log b n • ªª log ª b • c = log b + log c ªª log b / log b c = ª - ª log cª ⁿ log b m = m / n • ª log bª ÷ log b = 1 b log aª b log log b • c • d = c log log d ªª log b = c ÷ c log b log aUses of logarithms
Logarithms are often used to solve the equations that rank is unknown. Derivatives are easy to find and is therefore often used as the logarithm of the integral solution. In the equation bn = x, b can be found by rooting, n with logarithms, and x with an exponential function.Science and engineering
In science, there are many quantity that is generally expressed by logarithms. Why, and examples of a more complete, can be viewed on a logarithmic scale.

    The negative of the logarithm base 10 is used in chemistry to express hydronium ion concentration (pH). For example, the concentration of hydronium ion in water is 10-7 at 25 ° C, so that the pH 7.

    Unit bell (with symbol B) is a unit of measure of comparison (ratio), as comparison of the power and voltage. Most are used in telecommunications, electronics, and acoustics. One reason for the use of logarithms is due to the human ear perceives sound to be heard is logarithmic. Unit Bel called for the services of Alexander Graham Bell, the inventor in the field of telecommunications. Decibels (dB), which is equal to 0.1 bel, is more commonly used.

    The Richter scale measures the intensity of earthquakes using a base 10 logarithmic scale.

    In astronomy, the magnitude of the measured brightness of stars using a logarithmic scale, because the human eye perceives light is logarithmic.
Calculation easier
Logarithmic shift the focus from the calculation of normal numbers to rank-rank (exponent). When the logarithm base the same, then some kind of calculation becomes easier to use logarithms ::Calculations with numbers with exponents Identity Logarithmic Counting\! \, Ab \! \, A + B \! \, \ Log (ab) = \ log (a) + \ log (b)\! \ Frac {a} {b} \! \, A - B \! \, \ Log (\ frac {a} {b}) = \ log (a) - \ log (b)\! \, A ^ b \! \, A b \! \, \ Log (a ^ b) = b \ log (a)\! \, \ Sqrt [b] {a} \! \, \ Frac {A} {b} \! \, \ Log (\ sqrt [b] {a}) = \ frac {\ log (a)} {b}
The above properties make the calculation easier exponents, logarithms and use is very important, especially before the advent of calculators as a result of the development of modern technology.
To mengkali two numbers, which is needed is to look at the logarithm of each number in the table, summing, and see antilog amount in the table. For counting the rank or the root of a number, logarithm of the number can be seen in the table, then just divide by the radix mengkali or rank or roots.Calculus
The derivative is a logarithmic function

    \ Frac {d} {dx} \ log_b (x) = \ frac {1} {x \ ln (b)} = \ frac {\ log_b (e)} {x}
where ln is the natural logarithm, ie e-based logarithm. If b = e, then the above formula can be simplified into

    \ Frac {d} {dx} \ ln (x) = \ frac {1} {x}.
Integral logarithmic function is

    \ Int \ log_b (x) \, dx = x \ log_b (x) - \ frac {x} {\ ln (b)} + C = x \ log_b \ left (\ frac {x} {e} \ right) + C
Integral-based logarithm e is

    \ Int \ ln (x) \, dx = x \ ln (x) - x + C \,
For example, find the derivative

    \ Log (x)
Calculating the value of the logarithm
Logarithm to the base b can be calculated by the formula below.

    \ Log_b (x) = \ frac {\ log_e (x)} {\ log_e (b)} \ qquad \ mbox {or} \ qquad \ log_b (x) = \ frac {\ log_2 (x)} {\ log_2 ( b)}
As for the e-based logarithm and base 2, there are common procedures, which only use addition, subtraction, pengkalian, and division.