SOLUTION: HI I need to find the inverse function of h(x)=log(6x+5/2x-4) and I am just a little lost

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Question 976679: HI I need to find the inverse function of h(x)=log(6x+5/2x-4) and I am just a little lost
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
To find the inverse use x,y nomenclature.
y=log%28%28%286x%2B5%29%2F%282x-4%29%29%29
Interchange x and y and solve for y.
That new y is the inverse.

10%5Ex=%286y%2B5%29%2F%282y-4%29
6y%2B5=2%2A10%5Ex%2Ay-4%2A10%5Ex
6y-2%2A10%5Ex%2Ay=-5-4%2A10%5Ex
y%286-2%2A10%5Ex%29=-5-4%2A10%5Ex
y=-%285%2B4%2A10%5Ex%29%2F%286-2%2A10%5Ex%29
y=-%281%2F2%29%28%285%2B4%2A10%5Ex%29%2F%283-10%5Ex%29%29
h%5E%28-1%29%28x%29=-%281%2F2%29%28%285%2B4%2A10%5Ex%29%2F%283-10%5Ex%29%29