SOLUTION: I don't understand what ln(natural log) means. This is what I have so far: 15,000 = 10,000e ^.10t 15,000/10,000 = 10,000e^.10t/10,000 15000/10000 = e^.10t 1.5 = e ^.10

Question 33616: I don't understand what ln(natural log) means. This is what I have so far: 15,000 = 10,000e ^.10t
15,000/10,000 = 10,000e^.10t/10,000
15000/10000 = e^.10t
1.5 = e ^.10t
ln(1.5) = ln(e ^.10t)
Thanks,
Joey Widener
Found 2 solutions by Nate, venugopalramana:
Answer by Nate(3500) (Show Source): You can put this solution on YOUR website!
let us first run through the common log
the common log has a base of ten, so the log 10 = 1
Natural logs are logarithms with the natural base of 'e', so ln e = 1
Also, the power property of logarithms shows this: log x^2 .. is also.. 2 log x
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15,000/10,000 = 10,000e^.10t/10,000
15000/10000 = e^.10t
1.5 = e ^.10t
ln(1.5) = ln(e ^.10t)
ln(1.5) = .10t ln(e) use the power property and natural log of e is 1
ln(1.5)/.10 = .10t/.10 divide by .10
t is about 4.0547
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
IF BASE B TO THE POWER OF P IS X....... WRITTEN AS B^P=X....THEN WE SAY....
LOGARITHM (LOG IN SHORT) OF X TO BASE B IS P....WRITTEN AS .....LOG(X) TO BASE B =P
WE CAN HAVE ANY NUMBER AS BASE EXCEPT OFCOURSE 0 OR 1 OR NEGATIVE NUMBER SINCE FOR EXAMPLE.... 1 TO THE POWER OF ANY THING YOU GET 1 ONLY AND NOT X AS DESIRED.
FOR THE PURPOSE OF STANDARDISATION 2 STANDARD BASES ARE ADOPTED
1...BASE 10.....LOGS TO BASE 10 ARE WHAT WE NORMALLY USE.STANDARD TABLES ARE MADE OR USING CALCULATORS/COMPUTERS YOU CAN FIND THEIR VALUES.
EX.....10^2=100....SO LOG (100) TO BASE 10 =2
2....BASE E..THIS IS A SPECIAL NUMBER EQUAL TO ABOUT 2.8 APPROXIMATELY,WHICH IS FOUND IN MATHS QUITE OFTEN LIKE PI=3.14 YOU KNOW IN CIRCLES ETC..
LOGS TO BASE E ARE CALLED NATURAL OR NAEPERIAN LOGS.STANDARD TABLES ARE MADE OR USING CALCULATORS/COMPUTERS YOU CAN FIND THEIR VALUES.
EX...E^0=1...SO LN(1) TO BASE E =0...HERE LN IS USED INSTEAD OF LOG TO DISTINGUISH BETWEEN THE TWO...THOUGH NOT ALL USE THIS DISTINCTION.IT HAS TO BE UNDERSTOOD FROM CONTEXT.
FRANKLY YOUR OTHER PART OF QUESTION IS NOT CLEAR...WHAT DO YOU WANT?
THE SAME FORMULAE APPLY TO ANY BASE LOGS.SO IF YOU ARE FAMILIAR WITH BASE 10,YOU CAN USE THOSE FORMULAE FOR BASE E TOO.
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