document.write( "Question 1153723: Write a logarithmic equation \r
\n" ); document.write( "\n" ); document.write( "Use
\n" ); document.write( "f(x) = log5(x)
\n" ); document.write( " as the parent function. Ordered pair (-3,-2)
\n" ); document.write( "y =
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Algebra.Com's Answer #776005 by greenestamps(13203)\"\" \"About 
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\n" ); document.write( "We can have function(s) of the form

\n" ); document.write( "\"log%285%2C%28x%2Bb%29%29%2Bc\"

\n" ); document.write( "Given that the function is to have an integer value at x=-3, we want -3+b to be a power of 5.

\n" ); document.write( "(a) first example
\n" ); document.write( "5^0 = 1; -3+b = 1 --> b = 4

\n" ); document.write( "\"log%285%2C%28-3%2B4%29%29+=+log%285%2C1%29+=+0\"

\n" ); document.write( "We want the function value at -3 to be -2, so we need to subtract 2. Our first function that satisfies the requirements is

\n" ); document.write( "\"log%285%2C%28x%2B4%29%29-2\"

\n" ); document.write( "A graph (window -10 to 10; -5 to 2):

\n" ); document.write( "\"graph%28400%2C400%2C-10%2C10%2C-5%2C2%2Clog%285%2C%28x%2B4%29%29-2%29\"

\n" ); document.write( "(b) second example
\n" ); document.write( "5^1 = 5; -3+b = 5 --> b = 8

\n" ); document.write( "\"log%285%2C%28-3%2B8%29%29+=+log%285%2C5%29+=+1\"

\n" ); document.write( "We want the function value at -3 to be -2, so we need to subtract 3. Our second function that satisfies the requirements is

\n" ); document.write( "\"log%285%2C%28x%2B8%29%29-3\"

\n" ); document.write( "A graph (window -10 to 10; -5 to 2), showing both graphs passing through (-3,-2):

\n" ); document.write( "

\n" ); document.write( "We can also have functions of the form

\n" ); document.write( "\"a%2Alog%285%2C%28x%2Bb%29%29\"

\n" ); document.write( "Again using b=8,

\n" ); document.write( "\"log%285%2C%28-3%2B8%29%29+=+log%285%2C5%29+=+1\"

\n" ); document.write( "We want the function value to be -2 at x=-3; so we can multiply this function by -2. Our third function that satisfies the requirements is

\n" ); document.write( "\"%28-2%29%2Alog%285%2C%28x%2B8%29%29\"

\n" ); document.write( "A graph again, showing the graphs of all three functions passing through (-3,-2):

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\n" ); document.write( "You should be able to see that we can get as many functions as we want that satisfy the requirement.

\n" ); document.write( "Here is one more that gives the value -2 at x=-3:

\n" ); document.write( "\"%28-5%29%2Alog%285%2C%28x%2B8%29%29%2B3\"

\n" ); document.write( "One more graph, showing all four functions passing through (-3,-2):

\n" ); document.write( "
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