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Comment on Equation with Powers of 11
I got the same result but
(11^6)(11^6)/(11^8)(11^4k)=1/(11^3)
(11^-2)(11^6-4k)=(11^-3) then I solved for k in the equation
-2+6-4k=-3
4k=6+3-2
k=7/4
That works also!
That works also!
All of your steps are perfectly sound, because you correctly applied the exponent rules.
Nice job!
If we had to guess, could we
That's a good idea, but that
That's a good idea, but that strategy won't always work.
Consider this equation: (2^-10)/(2^x) = 1/(2^7)
This has similar elements to the question in the video, so we might conclude (incorrectly) that x must be positive.
However, in this case, x = -3
Sorry if this is obvious, but
12 - (8 + 4k) = 4 - 4k
12 - (8 + 4k) = 4 - 4k
We start with 12 (and zero k's).
From this amount, we're subtracting (8 + 4k)
That is, we're subtracting positive 8 AND we're subtracting positive 4k
12 MINUS 8 equals positive 4
zero k's MINUS 4k equals negative 4k
For more on this, start watching the following video at 3:58
https://www.greenlighttestprep.com/module/gre-algebra-and-equation-solvi...
Cheers,
Brent
Hi, why can't we cross
I tried it, got the wrong answer but i would like to know why can't we cross-multiply?
We can definitely cross
We can definitely cross multiply here.
Given: (11⁶)²/(11² x 11^k)⁴ = 1/11³
Cross multiply to get: (11⁶)²(11³) = (1)(11² x 11^k)⁴
Simplify the left side: 11¹⁵ = 11^(8 + 4k)
Since the bases are equal, the exponents must be equal.
So we have: 15 = 8 + 4k
Solve: k = 7/4