Question 916868: Confused about this logarithm
Suppose log a = 0.3, log b = -0.5. Evaluate
log(1000 aČ)
= log(1000) + log(aČ)
= 3 + 2 log(a)
= 3 + 2*0.3
= 3.6
I understand everything up until 3+2log(a) after that why does the 2 log(a) become only 0.3? since 1000 becomes 3 due to log(base 10) 1000 = 3. Wouldn't the same be true for 2log(a) being something like 2log(base 10)(0.3) and then getting a different answer other than 0.3?
Please help thanks!
Found 3 solutions by Alan3354, stanbon, Theo:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Suppose log a = 0.3, log b = -0.5. Evaluate
log(1000 aČ)
= log(1000) + log(aČ)
= 3 + 2 log(a)
= 3 + 2*0.3
= 3.6
I understand everything up until 3+2log(a) after that why does the 2 log(a) become only 0.3? ****************
It doesn't, it's 2 times 0.3
===========================
since 1000 becomes 3*********** 1000 doesn't become 3. Log(1000) = 3 ********* due to log(base 10) 1000 = 3. Wouldn't the same be true for 2log(a) being something like 2log(base 10)(0.3) and then getting a different answer other than 0.3?
It's 2 times, = 0.6. You entered it yourself.
Your answer is correct.
Answer by stanbon(75887)  (Show Source):
You can put this solution on YOUR website! Suppose log a = 0.3, log b = -0.5. Evaluate
log(1000 aČ)
= log(1000) + log(aČ)
= 3 + 2 log(a)
-------
2*log(a) = 2*0.3 = 0.6
-------------------------------
= 3 + 2*0.3
= 3 + 0.6
------
= 3.6
==============
Cheers,
Stan H.
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Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! you are given that log(a) is equal to .3
therefore 2 * log(a) has to be equal to 2 * .3 = .6
looking at log(a) = .3, you can solve for a because:
log(a) = .3 if and only if 10^.3 = a
this makes a = 1.995262315.
log(a^2) is therefore equal to log(1.995262315^2) which is also equal to 2 * log(1.995262315)
log(1.995262315^2) = .6
2*log(1.995262315) = .6
.6 is the right number.
log(1000) = 3 because 10^3 = 1000
log(a^2) = .6 because = 10^.6 = 3.981071706 which should be equal to a^2.
take the square root of 3.981071706 and you get 1.99526315
if that's what you were supposed to do in the problem, then you did it right.
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