# explain logarithms ?

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Logarithms simplify elaborated calculations and they are applied not only inside mathematical field, but other scientifical fields such that: chemistry (pH), biology(nautilus' shell), Earth science, psychology, astronomy, music.

The idea of function helps in the thorough study of logarithms.

The exponent to which a base a is raised is the logarithm of the number that results raising the base "a" to the exponent.

Solving for x the exponential equation `a^x = y` , came up with this conclusion.

`a^x = y =gt x*log_a (a) = log_a (y)`

But `log_a (a) = 1 =gt x = log_a (y)`

`` `a^(log_a (y)) = y`

**The solution to this equation, `x = log_a (y), ` is unique.**