SOLUTION: If the graph of the logarithmic function f(x) = log base 2 (5x+b) passes through the point (2,3), what is b?

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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?
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
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:
%283%29+=+log%282%2C+%285%282%29+%2B+b%29%29
We can solve this for b, First let's simplify:
3+=+log%282%2C+%2810+%2B+b%29%29
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:
2%5E3+=+10%2Bb
which simplifies to:
8+=+10+%2B+b
Now we just subtract 10:
-2+=+b