Sarah F.

asked • 05/25/17

Simplify ln(3((x^2)+1)) into a polynomial

Not necessarily the answer, just confused as to what the question is asking me! So if possible steps to arrive at the answer would be much appreciated! Thank you!
 
rewritten: 
simplify into a polynomial: 
 
ln(3(x^2)+1)

1 Expert Answer

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Arturo O. answered • 05/25/17

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ln(3x2+1) = ln(3x3) = ln3 + ln(x3) = ln3 + 3 lnx
 
It is not a polynomial.  It is a logarithmic expression in x.
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Sarah F.

Thank you! But I apologize, my typing was off (edited now)
 
It should read ln(3^((x^2)+1)), 3 to the power of (x squared + 1)
 
The simplify into a polynomial is what is throwing me. But that's how it's worded in the problem.
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05/25/17

Arturo O.

Let us work the revised, edited version of the problem:
 
y = ln[3(x^2 + 1)] = (x2 + 1) ln3 = (ln3)x2 + ln3
 
There is your polynomial in x, in this case a quadratic function of the form
 
y = ax2 + bx + c, 
 
where
 
a = ln3
b = 0
c = ln3
 
 
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05/25/17

Arturo O.

I am not sure if that is what they had in mind, but at least we got to a polynomial in x.
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05/25/17

Sarah F.

Excellent, thank you so much for your help! Seems there was a ln property I was overlooking there.
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05/25/17

Arturo O.

It is good to memorize these properties of logarithms (true for any base):
 
log(xy) = log(x) + log(y)
 
log(x/y) = log(x) - log(y)
 
log(xy) = y log(x)
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05/25/17

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