%path = "maths/functions/log" %kind = chindnum["texts"] %level = 10
The power operation generates a result from the basis and the exponent. So from the result there are two ways back: either to the basis or to the exponent.
To get the basis one forms the power of the result with the reciprocal of the exponent, e.g. \((3^2)^{\frac{1}{2}} = 3\). This is also called root.
To get the exponent there is the logarithm, e.g. \(\log_{3}(3^2)=2\).
From the calculation rules of exponents with same basis, e.g. \(2^32^2=2^{3+2}\) and \(\frac{2^3}{2^2}=2^{3-2}\) follow the logarithm rules that make plus out of multiply and minus out of divide.
The repetition of multiplication (power) becomes repetition of addition (multiplication).
From the last rule it follows how to calculate any logarithm with just one logarithm.
An exponential equation, i.e. an equation that has the unknown in the exponent, is solved best by first trying to bring it into the form \(b^x = d\) and then apply the logarithm on both sides.
The logarithm always refers to a basis. If the basis is not specified, then \(\log\) is either with Basis 10 or with basis e=2.71828182846… (Euler number)
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