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explain what is meant by a logarithm. state and use the laws of logarithms. solve simple equations requiring the use of logarithms. Contents. Introduction. Why do we study logarithms ? What is a logarithm ? if x = an then loga x = n. 4. Exercises. 5. The first law of logarithms. loga xy = loga x + loga y. 6. The second law of logarithms.
Logarithms. This booklet explains what is meant by a logarithm. It states and illustrates the laws of llogarithms. It explains the standard bases 10 and e. Finally it shows how logarithms can be used to solve certain types of equations.
4 Αυγ 2024 · Logarithm is a mathematical function that represents the exponent to which a fixed number, known as the base, must be raised to produce a given number. In other words, it is the inverse operation of exponentiation.
What is a Logarithm? Given some POSITIVE real numbers x and b where b = 1, The logarithm of x to the base b. is. the power that you have to raise b to in order to get x . So if the logarithm is L, then. bL = x . We write L = log x . b. So. blogb x = x . NOTES. The textbook requires b > 1, but this is not necessary for the definition.
In chemistry, pH is a logarithmic measure for the acidity of an aqueous solution. Logarithms are commonplace in scientific formulae, and in measurements of the complexity of algorithms and of geometric objects called fractals.
A logarithm is the inverse of the exponential function. Specifically, a logarithm is the power to which a number (the base) must be raised to produce a given number. For example, \(\log_2 64 = 6,\) because \( 2^6 = 64.\) In general, we have the following definition: \( z \) is the base-\(x\) logarithm of \(y\) if and only if \( x^z = y \). In ...
The logarithm was a mysterious number which we found from looking up a table in a “log book” (which also contained sine, cosine and other interesting functions). The properties used in calculation were — log(a × b) = log a + log b. log(a/b) = log a − log b. log ab = b × log a √ log( b a) = (log a)/b.
