Try to relax. Your desperation has surely progressed to the point where
you're unable to think clearly, and to agonize over it any further would only
cause you more pain and frustration.
I've never seen this kind of problem before. But I arrived here in a calm state,
having just finished my dinner and spent a few minutes rubbing my dogs, and
I believe I've been able to crack the case.
Consider this: (2)^a negative power = (1/2)^the same power but positive.
So:
Whatever power (2) must be raised to, in order to reach some number 'N',
the same number 'N' can be reached by raising (1/2) to the same power
but negative.
What I just said in that paragraph was: log₂ of(N) = <em>- </em>log(base 1/2) of (N) .
I think that's the big breakthrough here.
The rest is just turning the crank.
Now let's look at the problem:
log₂(x-1) + log(base 1/2) (x-2) = log₂(x)
Subtract log₂(x) from each side:
log₂(x-1) - log₂(x) + log(base 1/2) (x-2) = 0
Subtract log(base 1/2) (x-2) from each side:
log₂(x-1) - log₂(x) = - log(base 1/2) (x-2) Notice the negative on the right.
The left side is the same as log₂[ (x-1)/x ]
==> The right side is the same as +log₂(x-2)
Now you have: log₂[ (x-1)/x ] = +log₂(x-2)
And that ugly [ log to the base of 1/2 ] is gone.
Take the antilog of each side:
(x-1)/x = x-2
Multiply each side by 'x' : x - 1 = x² - 2x
Subtract (x-1) from each side:
x² - 2x - (x-1) = 0
x² - 3x + 1 = 0
Using the quadratic equation, the solutions to that are
x = 2.618
and
x = 0.382 .
I think you have to say that <em>x=2.618</em> is the solution to the original
log problem, and 0.382 has to be discarded, because there's an
(x-2) in the original problem, and (0.382 - 2) is negative, and
there's no such thing as the log of a negative number.
There,now. Doesn't that feel better.
Bill and Amy travel the same distance from home to school of 14.4 kilometers. Amy takes 40 minutes of time to arrive to school which means she has a rate of 14.4 km /40 minutes or 6 meters/ second. Bill takes a total 60 minutes to arrive to school. Hence Bill's rate is equal to 14.4 km/60 minutes or 4 meters/ second.Amy's is 2 m/s faster than Bill's speed, then.
Answer:
Find the area of the larger rectangle, then subtract the area of the two smaller rectangles in the corners. Separate the figure into two or three rectangles, and add the areas.
Step-by-step explanation:
this is the sample response
Answer:
74.36 g of aluminium acetate.
730.27g of aluminium acetate.
- to the nearest hundredth.
Step-by-step explanation:
Acetic acid is usually written as CH3COOH.
a. 6CH3COOH + Al(OH)3 ---> Al(CH3COO)3 + 9H2O
So 6 moles of acetic acid produce 1 mole of aluminium acetate.
Using the molecular masses
6*( 1.008*4 + 12.011*2 + 16 *2) g acetic acid gives (26.98+3(36.032+ 2*12.011)
348.228 g acetic acid gives 207.142 g Al acetate.
So 125 g gives (207.142 / 348.228) * 125
= 74.36 g of aluminium acetate.
b.
(26.98 + 3*16 + 3 * 1.008) g of Al(OH)3 gives 207.142 g Al acetate
78.004 g gives 207.142 g Al acetate
275 g gives (207.142 / 78.004) * 275
= 730.27g Al acetate.
Answer:E
Step-by-step explanation:
