SOLUTION: Find the inverse function for f(x) = (lnx-5)/(2lnx+7)

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Question 1132903: Find the inverse function for f(x) = (lnx-5)/(2lnx+7)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Find the inverse function for
+f%28x%29+=+%28ln%28x%29-5%29%2F%282ln%28x%29%2B7%29+

+y=+%28ln%28x%29-5%29%2F%282ln%28x%29%2B7%29+...........swap x and y

+x=+%28ln%28y%29-5%29%2F%282ln%28y%29%2B7%29+.......solve for y

+x%282ln%28y%29%2B7%29=+%28ln%28y%29-5%29+

+2xln%28y%29%2B7x=+ln%28y%29-5+

+2xln%28y%29-+ln%28y%29=-5+-7x

+%282x-+1%29ln%28y%29=-5+-7x

+ln%28y%29=%28-5+-7x%29%2F%282x-+1%29

Apply log rule: a=log%28b%2Cb%5Ea%29

+ln%28y%29=ln%28e%5E%28%28-5+-7x%29%2F%282x-+1%29%29%29->When the logs have the same base
highlight%28y+=+e%5E%28%28-5+-7x%29%2F%282x-+1%29%29%29