Show that the logarithmic function `f: R0+->R` given by `f(x)=(log)_a x ,\ a >0` is a bijection.

Explanation

We have to proof that given function is bijection

`f:R^+``->R` given by `f(x)=log_ax,a`>`0`
one−one:

Let` x_1`and `x_2` be any two elements in the domain (N), such that` f(x_1)=f(x_2)`.

Calculate `f(x_1)`:

`implies f(x_1)=log_ax_1`

​Calculate` f(x_2):`

`implies f(x_2)=log_ax_2`

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