Solve Logarithmic Problem: Evaluate & Simplify

  • Thread starter Thread starter lucky_star
  • Start date Start date
AI Thread Summary
The discussion revolves around evaluating and simplifying a logarithmic expression without a calculator. The initial steps involve combining logarithms and applying the laws of logarithms, leading to the expression 3 / log2(10). However, a notation error is identified in the simplification process, where the correct interpretation of the fraction is clarified. Participants emphasize the importance of proper notation in mathematical expressions to avoid confusion. Overall, the conversation highlights the need for accuracy in both calculations and notation when solving logarithmic problems.
lucky_star
Messages
33
Reaction score
0
Hi, I have a log problem. Can anyone please check if I did it correctly!?

Homework Statement


Evaluate the following using the laws of logarithms.
Simplify your answer as much as possible. (Note:
These should be done without a calculator).

[log(5)+log(2)] / log2(cubic root of 10)
= log(5*2) / log2 (10)1/3
= log(10) / 1/3*log2(10)
= 3 / log2(10)


Is this simplified correctly? Can we simplify more?
 
Physics news on Phys.org
Good.
 
Thank you!
 
Know this: Your notation is faulty near the end of your steps.

This, "= log(10) / 1/3*log2(10)" is not what you meant.
You really meant and should have written, log2(10)/(1/3)*log2(10)
 
That is because 1/ab is normally read as 1/(ab), not as (1/a) b.
 
Yes, that what I meant symbolipoint. Thank you everybody! I need to pay more attention on how I write it properly.
 
I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
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
Back
Top