SOLUTION: Which one has more value(or which is bigger?)? log2(3) or log3(8) Solve it without using calculator,please.

Algebra.Com
Question 955354: Which one has more value(or which is bigger?)? log2(3) or log3(8)
Solve it without using calculator,please.
Found 3 solutions by MathLover1, herosz, ikleyn:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

or .......change the base
or
or
or
so,
Answer by herosz(4)   (Show Source): You can put this solution on YOUR website!
Unfortunately MathLover1's answer is not self-evident!
for example assuming log3=2/3 and log2=1/3 (we don't use calculator so don't know the exact value) ==>
(2/3)*3>(3*1/3)*3/2 so log2(3)>log3(8) that is not true!
Answer by ikleyn(52797)   (Show Source): You can put this solution on YOUR website!
.
Which number is greater: or ?
~~~~~~~~~~~~~~~~~ 

We have, from one side,

 =  =  <  = 7.   Thus   < .



We have, from the other side,

 =  =  >  =  = 7.    Thus   > .



From these two inequalities,   <    and    > ,   you have     <  .



Answer.  We have proven    <    without using calculator.

QED.




RELATED QUESTIONS

Which one has more value(or which is bigger?)? log2(3) or log3(8) Solve it without using (answered by lwsshak3,herosz)
Solve without using calculator. Which one is greater log3 to the base 2 or log5 (answered by Alan3354,math_helper,herosz)
Without using a calculator or technology, determine which is bigger,... (answered by ikleyn)
Please sort these out?(which has the most value , which has the lowest value) *log2(3)* (answered by Theo)
Without using a calculator or computer, determine which is larger, 2^3000 or... (answered by richwmiller,CharlesG2)
Without using calculator or tables ,find the value of log3.6 given that log2 equer to... (answered by Boreal,MathTherapy)
Without using a calculator which is larger: x= 7^1/4 or y=4^1/3 (answered by Edwin McCravy)
Find the value of the expression without using a calculator. log3 3 + log3 27 - log3... (answered by Fombitz)
Without using a calculator, tell which is larger: the positive 6th root of 10 or the 3rd... (answered by stanbon,rapaljer)