Algebra

Logarithmic Functions

Graphs of Logarithmic Functions

         

Let ff be the translation f:(x,y)(x+m,y+n)f: (x,y) \to (x+m, y+n), where mm and nn are constants. If ff transforms the curve y=log23xy=\log_2 3x to y=log2(12x108)y=\log_2 (12x-108), what is m+n|m+n|?

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

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

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

For xx and yy satisfying x+y=8x+y=8, let mm be the maximum value of log4x+log4y.\log_{4}x+\log_{4}y. If aa and bb are the values of xx and yy, respectively, for which the maximum value is attained, what is m+2a+3bm+2a+3b?

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

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