The inequality \log_{a} f(x)<\log_{a} g(x) implies that

Question 48

The inequality $$\log_{a} f(x)<\log_{a} g(x)$$ implies that

Solution

If $$\log_ax<\log_ay$$, then both $$x$$ and $$y$$ are greater than 0, and -

For $$0<a<1$$ => $$x>y$$

For $$a>1$$ => $$x<y$$

We will replace x by f(x) and y by g(x).

If $$\log_af(x)<\log_ag(x)$$, then both $$f(x)$$ and $$g(x)$$ are greater than 0, and -

For $$0<a<1$$ => $$f(x)>g(x)>0$$

For $$a>1$$ => $$0<f(x)<g(x)$$

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