Question 48992: I need help with a problem.
I need to find an element in the domain of h(x)= log4(x-2) that coresponds with 1, a member of the range.
Answer by Born2TeachMath(20)   (Show Source):
You can put this solution on YOUR website! You have the function h(x) = log4 (x-2).
You need to find the domain element that corresponds the range element of 1, or in notation, you need to find the x where h(x) = 1.
Therefore, set log4 (x-2) = 1, and solve for x.
To remove the log4, we apply the inverse function exponential base 4 to both sides:
4^(log4 (x-2)) = 4^(1)
The exponential base 4 and the log base 4 are inverse functions, and they "undo" eachother, like squares "undoing" square roots, and multiplication undoing division. Therefore, you're left with
(x-2) = 4^1
4^1 equals 4, so
(x-2) = 4.
Add 2 to both sides,
(x - 2) + 2 = 4 + 2
and we have x = 6.
The last thing we must check is if the solution is in the domain of the function h(x). All log functions can only work on positive number inputs (try positive, negative, and zero inputs on your calculator using the "log" or "ln" buttons!) Therefore, checking x=6 as the input, we have
h(6) = log4 (6-2).
And since 6-2 is positive, it works in the log4 function, with a range value of 1.
Don't forget to check that your solution works in the domain of the given function (only positive numbers work in log functions - teacher like to throw these tricks onto quizzes and tests - I know I do.
Good luck!
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