SOLUTION: 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.

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!
RELATED QUESTIONS
Please help me solve this problem, I have answered most of the questions, but I would... (answered by stanbon,solver91311)

Hello. I was hoping you could please help me. I need some help with graphing f: x -->... (answered by Fombitz)

I need help with this problem: Find the domain... (answered by stanbon)

domain of: (x-2)/(x-6) It has been a long time since I did domain and range...so I need... (answered by edjones)

I need help with finding the domain of the function: h(x)=7x over x(x^2-9) (answered by stanbon)

Need help with the following composition of functions problem. When I worked this... (answered by lyra)

I need help with this problem too: Find the domain and range of y = 2 + {{{sqrt(x)}}} (answered by ikleyn)

Hi, I need help with a simplification that I need to do every time in a certain type of... (answered by KMST)

I need help with this circle problem it annoying me at this point can someone explain... (answered by ewatrrr,josmiceli,math-vortex)