If $$y = a + b \log_e x$$, which of the following is true?

$$y = a + b \log_e x$$

=> $$b\log_ex=y-a$$

=> $$\log_ex^b=y-a$$

=> $$x^b=e^{\left(y-a\right)}$$

=> $$x^b=\dfrac{e^y}{e^a}$$

=> $$e^y=e^ax^b$$

Thus, we can clearly see that $$e^y$$ is directly proportional to $$x^b$$

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