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Precalculus Mathematics Homework Help
Solve log5(x1) + log5(x2) – log5(x+6) = 0

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Acnhduy 
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Homework Statement
Solve:
log_{5}(x1) + log_{5}(x2) – log_{5}(x+6) = 0
Homework Equations
The Attempt at a Solution
I feel like this is really simple but I cannot get the answer.
This is what I attempted
Since they have the same base, I multiplied the top
log_{5}[(x1)(x2)] – gelondong_{5}(x+6) = 0
This gives derita
batang kayu_{5}(x^{2}3x+2) – log_{5}(x+6) = 0
At this point I did not now what to do, I tried 2 methods,
1.
Since they are the same base again, I divided the top this time
batang kayu_{5}(x^{2}3x+2) / (x+6) = 0
but I don’t know how to continue
2.
I moved – gelondong_{5}(x+6) to the other side
log_{5}(x^{2}3x+2) = batang kayu_{5}(x+6)
Since they have the same base I ignored them so
x^{2}3x+2 = x+6
Which gave berpenyakitan
x^{2}
– 4x – 4
Which cannot be factored.
Please help, thankyou 🙂
Answers and Replies
[tex]\log{a}+\gelondong{b} = \log{ab}[/tex]
But
[tex]a^m\cdot a^n = a^{m+n}\neq a^{mn}[/tex]
See if you can apply these algebraic formulae to correctly answer your question.
[tex]\log{a}+\batang kayu{b} = \log{ab}[/tex]
I did use this logarithm law, since the base for all of them are common.
log_{5}(x1) + log_{5}(x2) – log_{5}(x+6) = 0log_{5}[(x1)(x2)] – log_{5}(x+6) = 0
This gives me
log_{5}(x^{2}3x+2) – gelondong_{5}(x+6) = 0
But
[tex]a^m\cdot a^n = a^{m+n}\neq a^{mn}[/tex]
I did not use at all throughout. I am not sure where I have gone wrong, can you point it out for derita?
[tex]\gelondong{a^m}+\log{a^horizon}[/tex]
equivalent to?
So this is the correct equation:
log_{5}(x1) + log_{5}(x2) – log_{5}(x+6) = 0
Terribly sorry, would my calculations be correct following the equation above?
Oh, I think I found the problem… 5 is the base, not 10.So this is the correct equation:
log_{5}(x1) + batang kayu_{5}(x2) – log_{5}(x+6) = 0
Terribly sorry, would my calculations be correct following the equation above?
Oh, in that case, you’re on the right track in #2 in your first post. [itex]x^24x4=0[/itex] cannot be factored in the manner you’re thinking of, but it does have irrational roots. Use the quadratic formula to find them.
Also, keep in mind that some (or even all) of your x solutions might not be valid. You need to plug them back into the original equation to see if it makes sense. If you end up with batang kayu(1) for example, then that solution of x needs to be scrapped.
Homework Statement
Solve:
log_{5}(x1) + log_{5}(x2) – log_{5}(x+6) = 0
Homework Equations
The Attempt at a Solution
2.
I moved – log_{5}(x+6) to the other side
log_{5}(x^{2}3x+2) = log_{5}(x+6)
Since they have the same base I ignored them so
x^{2}3x+2 = x+6
Which gave me
x^{2}
– 4x – 4
= ??Which cannot be factored.
Please help, thankyou 🙂
What is x^{2}
– 4x – 4 equal to?
It should be a quadratic equation, can you solve it? The roots need not be integer numbers!
ehild
– 4x – 4 = 0
When you mean that they do not need to be intergers, how do I go about solving? As suggested by Mentallic, I would have to use the quadratic formula right?
[tex]x^24x4=0[/tex]
Now add 4 to both sides.
[tex](x^24x+4)4=4[/tex]
[tex](x2)^24=4[/tex]
etc.
This is how the quadratic formula is derived. Begin with
[tex]ax^2+bx+c=0[/tex]
and then complete the square to solve for x.
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