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# Given that log_4n 40sqrt3 = log_3n 45, find n^3.

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Given that log_4n 40sqrt3 = log_3n 45, find n^3.

waffles  Feb 23, 2018
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log_4n 40sqrt3 = log_3n 45, solve for n

log(40sqrt(3))log(3n) =log(45)log(4n)

1.840620log(3n) = 1.653213log(3n) divide both sides by 1.6532131

1.11335996log(3n) =log(4n)

Solve for n:

(log(n) + log(4))/(log(n) + log(3)) = 1.11336

Simplify and substitute x = 1/(log(n) + log(3)).

(log(n) + log(4))/(log(n) + log(3)) = (log(4/3))/(log(3) + log(n)) + 1

= x log(4/3) + 1:

log(4/3) x + 1 = 1.11336

Subtract 1 from both sides:

log(4/3) x = 0.113359

Divide both sides by log(4/3):

x = 0.394043

Substitute back for x = 1/(log(n) + log(3)):

1/(log(n) + log(3)) = 0.394043

Take reciprocals of both sides:

log(n) + log(3) = 2.5378

Subtract log(3) from both sides:

log(n) = 1.43918

Cancel logarithms by taking exp of both sides:

n = 4.21725, n^3 =~75

Guest Feb 23, 2018
edited by Guest  Feb 23, 2018
edited by Guest  Feb 23, 2018
#3
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I see you’ve thrown more slop on it –Surprise, Surprise!

By the way Mr. BB, n^3 is exactly 75; the (n =4.21725) should be approximate.

GingerAle  Feb 23, 2018
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Mr. BB, your presentation is SLOP. Anyone who can figure out the solution from your slop does not need the slop in the first place.

$$\log_{4n} 40\sqrt{3} = \log_{3n} 45\\ \text{Antilog form }\\ 4^x n^x=40\sqrt{3}\\ 3^x n^x=45\\ \left(\dfrac{4}{3}\right)^x=\dfrac {1}{9}*{8\sqrt{3}} = \dfrac{8}{3\sqrt 3}\rightarrow x=\dfrac {3}{2}\\ 8n^{\frac {3}{2}}=40\sqrt 3\\ n= 3^{\frac13} * 5^{(\frac23)} \rightarrow n^3= 3 * 5^2 =75$$

Tell me, Mr. BB, do you actually find diamonds in SLOP, or do you find a diamond and throw SLOP on it? (Like, I don't already know.)

GA

GingerAle  Feb 23, 2018
#4
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http://www.pleacher.com/mp/probweek/p2003/a011303.html

https://web2.0calc.com/questions/andy

[plagiarized?  Or was it conjured from "Set Theory"? As phony as a 3-dollar bill !. Utterly Shameless!]

Guest Feb 23, 2018
edited by Guest  Feb 23, 2018
edited by Guest  Feb 23, 2018
edited by Guest  Feb 23, 2018
#5
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Long ago, your ship sailed and sank. No one thought it worthy of salvage— then or now.  It needs warning buoys because of the toxic waste that it leaches.

An arsonist thinks all fires start because of arson.

A thief thinks all missing items are stolen.

An embezzler thinks any missing funds are embezzled.

A plagiarist thinks every posted solution is plagiarized.

I wasn’t accusing you of plagiarism, Mr. BB. However, you didn’t cite the Mathematica program from which you copied your pasted SLOP.  The slipper fits because it belongs to you. You are what you are, Mr. BB.

You are gifted Mr. BB, you are the only person I know that takes a brilliantly integrated mathematical program and finds a noxious use for it.  Another example of throwing slop on a diamond.

GA

GingerAle  Feb 23, 2018
#6
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https://math.stackexchange.com/questions/1897276/log-4n-40-sqrt3-log-3n-45-find-n3

{YOU ARE NOT ONLY A PHONY BUT A FLAGRANT PLAGIARIST AND A PATHOLOGICAL LIAR!!  SHAME ON YOU!!].

Guest Feb 24, 2018
edited by Guest  Feb 24, 2018

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