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Comment on Solving Equations with Exponents
Hi Brent!
how to factorize this, x^3 - 9x^2 + 26x - 24 = 0, i have come across this question in one of the greprep club test.
Can you provide the entire
Can you provide the entire question?
Factoring that expression is beyond the scope of the GRE, so I have a feeling that we can solve the question using other methods.
ASIDE: x^3 - 9x^2 + 26x - 24 = (x - 2)(x - 3)(x - 4). But, as I said, the technique I used is BEYOND the scope of the GRE, and is not needed on test day.
The solutions of x3−9x2+26x
Indicate all possible values.
-2
-1
2
3
4
5
Factorizing above equation takes lot of time. i saw some question in which we need to employ sine function to find length of triangle, are all these are out of GRE scope?
I suppose that there exists
I suppose that there exists an uncomplicated solution to the question. It involves PLUGGING in each answer choice to see if it satisfies the given equation. That said, that kind of solution is too tedious for the GRE.
The alternative solution involves a bunch of algebra that is not required for the GRE. So, I'd just ignore the question.
Also, any question that can be solved only through the application of the sine function is also out of scope.
Can you help me in this
Thank you
9^x - 9^(x-2) = 240 then x(x - 1/2) =
A) 3
B) 4
C) 5
D) 6
E) 9
Take: 9^x - 9^(x-2) = 240
Take: 9^x - 9^(x-2) = 240
Factor out the smallest power to get: 9^(x-2)[9² - 1] = 240
Simplify to get: 9^(x-2)[81 - 1] = 240
Simplify to get: 9^(x-2)[80] = 240
Divide both sides by 80 to get: 9^(x-2) = 3
Rewrite 9 as 3² to get: (3²)^(x-2) = 3
Simplify to get: (3)^(2x-4) = 3^1
So, it must be true that: 2x-4 = 1
Add 4 to both sides: 2x = 5
Solve: x = 2.5
So, x(x - 1/2) = 2.5(2.5 - 0.5)
= 2.5(2)
= 5
Answer: C
I dont understand the
The exceptions are related to
The exceptions are related to whether the EXPONENTS in an EQUATION are equal.
So, if we have 2^x = 2^3, we can be certain that x = 3.
In other words, since we have an EQUATION where are the bases are the same (and the base isn't 1, -1 or 0), then we can conclude that the EXPONENTS (x and 3) are equal.
In your example, 2^3 vs 2^4, we don't have an equation, and we aren't making any conclusions about the exponents.
All we're saying is that 2^3 does not equal 2^4.
This conclusion doesn't have anything to do with the exceptions.
Does that help?
Hi Brent! question by
Hi Wasi,
Hi Wasi,
In the future, please include the hyperlink to the question.
I have added a second solution here: https://gre.myprepclub.com/forum/if-5-13-9-7-3-15-x-what-is-the-value-of...
Does that help?
What is the value of N such
Can you help with the above? I understand I have to get two identical bases but I just dont understand the step required when dealing with a negative base.
The quick solution is to
The quick solution is to recognize that (-2)^4 = 16 [since (-2)(-2)(-2)(-2) = 16]
So, our original equation becomes: (−2)^(2N) = [(-2)^4]^2
Apply the power of a power law to the right side: (−2)^(2N) = (-2)^8
At this point we can see that 2N = 8, which means N = 4
Another possible approach uses this property: x^(ab) = (x^a)^b
Note: This is just the power of a power law.
We can apply this property to rewrite the left side: [(−2)^2]N = 16^2
Simplify the part in the square parentheses: [4]^N = 16^2
Now replace 16 with 4^2 to get: 4^N = (4^2)^2
Simplify the right side to get: 4^N = 4^4
Once again N = 4
Does that help?