Question

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Explain Logarithmic function with suitable diagram...

Answer 1

$\bold{Logarithmic \:Function}$

Logarithmic functions are the inverses of exponential functions. The inverse of the exponential function y = ax is x = ay.

Answer 2

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$\large{Logarithmic\:Functions}$

A logarithm is simply an exponent that is written in a special way.

For example, we know that the following exponential equation is true:

$3 {}^{2} = 9$

In this case, the base is 3 and the exponent is 2. We can write this equation in logarithm form (with identical meaning) as follows:-

$log_{3}(9) = 2$

We say this as "the logarithm of 9 to the base 3 is 2". What we have effectively done is to move the exponent down on to the main line. This was done historically to make multiplications and divisions easier, but logarithms are still very handy in mathematics.

The logarithmic function is defined as:

$\boxed{f(x) = log_{b}(x)}$

The base of the logarithm is b.

The 2 most common bases that we use are base 10 and base e, which we meet in Logs to base 10and Natural Logs (base e) in later sections.

The logarithmic function has many real-life applications, in acoustics, electronics, earthquake analysis and population prediction.