Question 1130719: 10^4logx - 7(10^2logx) + 10 = 0
Found 5 solutions by Alan3354, MathLover1, ikleyn, greenestamps, MathTherapy:
Answer by Alan3354(69443)   (Show Source):
Answer by MathLover1(20850)  (Show Source):
Answer by ikleyn(52812)  (Show Source):
You can put this solution on YOUR website! .
Much more shorter and straightforward solution is possible.
First, since "x" is under the logarithm function, it must be positive: x > 0.
So, the domain for this equation is the set {x | x > 0 }.
Second,  = x; therefore, the original equation in the domain x > 0 is equivalent to this simple equation
 = 0.
Factor left side:
(x^2-5)*(x^2-2) = 0.
Formally, it has 4 solutions  ,  ,  and  .
Of these, only positive numbers belong to the domain, so the answer is these two numbers and .
Solved.
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Regarding the post by @MathLover1, notice that the negative and are not the solutions.
To count them among the solutions, as @MathLover1 does, is a rude mistake.
The way on how @MathLover1 solves the problem is ANTIPEDAGOGIC.
When the student presents the solution in this way, he (or she) simply demonstrates that he (or she)
does not know the basic properties of logarithms.
The lesson to learn from my solution is THIS :
the problem in the post is designed and intended to be solved in the way as presented.
/\/\/\/\/\/\/\/\/
I don't know for what reason the tutor @greenestamps kicks me and my solution, which is absolutely correct.
Simply ignore/disregard his post in the part which relates to my solution.
In the future, to avoid misunderstanding and ambiguity, write your formulas using parentheses like this:
10^(4*logx) - 7*(10^(2*logx)) + 10 = 0.
It is the plain text format, which is uniquely appropriate format for posting to this forum.
It corresponds to this form of the equation
 -  +  = 0.
Answer by greenestamps(13203)  (Show Source):
You can put this solution on YOUR website!
Although the solution by tutor @ikleyn is probably correct for the INTENDED problem, it has nothing to do with the problem as presented.
In the expression "10^4logx" there are two operations -- an exponentiation and a multiplication. In standard order of operations, exponentiation is done first. So the equation as you show it is
To solve this equation....
which to 6 decimal places is 0.997527.
The intended equation is almost certainly
Please be polite when you post questions: use parentheses where required so we don't need to guess what the real question is.
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I have to respond to the absurd comments tutor @MathTherapy made about my response....
In my response, I acknowledged that the PROBABLE intent of the problem was with the equation
But I also pointed out that, as the problem is presented, it is something very different, with a very different solution.
And my response included a statement, intended for the person who submitted the problem, showing that the use of parentheses was important. That was a useful thing to include.
Tutor @MathTherapy's remarks about my response:
"He doesn't have much sense and just loves to criticize.
Plus, he thinks he knows everything."
My comments to his comments....
(1) I have enough sense to know for a fact that exponentiation has precedence over multiplication, and therefore the correct solution to the problem as presented is what I showed. Perhaps he doesn't know that....
(2) There is nothing about my response that can be characterized as a criticism. I presented an informative response that was intended to show that the use of parentheses is important.
As for loving to criticize, his answer is nothing but a criticism, along with a repetition of a solution already provided by another tutor.
Take a look at the answers he has provided in this forum and see how often his response is nothing but a criticism of another tutor, sometimes accompanied by an answer with no work shown, which doesn't help the reader learn anything.
Then decide for yourself who it is that loves to criticize.
Answer by MathTherapy(10555)  (Show Source):
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