Simplify logarithmic equations

AI Thread Summary
The discussion focuses on simplifying the logarithmic expression log2(1/8). One participant initially claims the answer is -3 but doubts its correctness. Another confirms that -3 is indeed the correct answer, explaining that log2(1/8) equals -3 because 2 raised to the power of -3 equals 1/8. The conversation also reflects frustration with a teacher's response. The correct simplification of the logarithmic equation is confirmed as -3.
hibachii
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Homework Statement



Simplify

log21/8


Homework Equations


-


The Attempt at a Solution


the answer i got was -3 but it is not right.
 
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hibachii said:

Homework Statement



Simplify

log21/8


Homework Equations


-


The Attempt at a Solution


the answer i got was -3 but it is not right.
-3 is the correct answer.

log2(1/8) = -3
This equation is equivalent to 2-3 = 1/8.
 
ok thanks. teacher is a douche
 

Thread 'Greatest possible value of a constant in polynomial'

Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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