document.write( "Question 421232: If the graph of the logarithmic function f(x) = log base 2 (5x+b) passes through the point (2,3), what is b? \n" ); document.write( "

Algebra.Com's Answer #294354 by jsmallt9(3758) $\"\"$ $\"About$

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If the given point is on the graph of the given equation, then the coordinates of the point must be a solution to the equation. (IOW: The coordinates must fit the equation.) So:
\n" ); document.write( " $\"%283%29+=+log%282%2C+%285%282%29+%2B+b%29%29\"$
\n" ); document.write( "We can solve this for b, First let's simplify:
\n" ); document.write( " $\"3+=+log%282%2C+%2810+%2B+b%29%29\"$
\n" ); document.write( "Now we rewrite the equation in exponential form. In general $\"log%28a%2C+%28p%29%29+=+q\"$ is equivalent to $\"a%5Eq+=+p\"$ . Using this pattern on our equation we get:
\n" ); document.write( " $\"2%5E3+=+10%2Bb\"$
\n" ); document.write( "which simplifies to:
\n" ); document.write( " $\"8+=+10+%2B+b\"$
\n" ); document.write( "Now we just subtract 10:
\n" ); document.write( " $\"-2+=+b\"$ \n" ); document.write( "

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