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## Logarithmic Functions

Logarithmic scales are used when the range of possible values is very wide, such as the intensity of an earthquake or the acidity of a liquid, in order to avoid the use of large numbers.

# Graphs

Let $$f$$ be the translation $$f: (x,y) \to (x+m, y+n)$$, where $$m$$ and $$n$$ are constants. If $$f$$ transforms the curve $$y=\log_2 3x$$ to $$y=\log_2 (12x-108)$$, what is $$m+n$$?

Which of the following could be the graph of $$\log_a {x} \:$$ if $$0<a<1 \:?$$

Which of the following could be the equation of the above graph?

(A) $$~ y = \log{|x|}$$
(B) $$~ y = \left|\log{|x|}\right|$$
(C) $$~ |y| = \log{x}$$
(D) $$~ y = |\log{x}|$$

For $$x$$ and $$y$$ satisfying $$x+y=8$$, let $$m$$ be the maximum value of $\log_{4}x+\log_{4}y.$ If $$a$$ and $$b$$ are the values of $$x$$ and $$y$$, respectively, for which the maximum value is attained, what is $$m+2a+3b$$?

Which of the following could be the graph of $$\log_a {x} \:$$ if $$0<a<1 \:?$$

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