Question 1042488: Approximate the logarithm using the properties of logarithms, given logb2=.3562, logb3=.5646, logb5=.8271
logb 12
logb (5b^4)
logb ^8sqrt(3b)
Found 3 solutions by stanbon, Theo, MathTherapy:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Approximate the logarithm using the properties of logarithms, given logb2=.3562, logb3=.5646, logb5=.8271
logb 12 = logb(4*3) = logb(4)+ logb(3) = 2log(2)+log(3) = 2(0.3562)+0.5646
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logb (5b^4) = logb(5) + 4logb(b) = 0.8271 + 4
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logb ^8sqrt(3b)
Question:: What does your ^ mean ??
Cheers,
stan H.
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Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! logb(2) = .3562
logb(3) = .5646
logb(5) = .8271
logb(x) = y if and only if b^y = x.
using this formula:
logb(2) = .3562 if and only if b^.3562 = 2
raise each side of the equation to the 1/.3562 power and you get:
(b^(.3562)^(1/.3562) = 2^(1/.3562)
simplify to get b = 7.000274846
do the same with the the other two and you will get b = 6.999...
since b has to the same value in all 3, then my guess is that b = 7.
using that guess, i got the answers indicated when i rounded to 4 decimal places.
for example:
log7(2) = .3562
log7(2) = log(2)/log(7) = .3562
evaluate log(2)/log(7) and you get .356207.....
round it to 4 decimal places and you get .3562.
i was able to get the other answers as well rounded to 4 decimal places when i assumed b = 7.
given that b = 7, the other problems should fall in line.
logb(12) becomes log7(12) which becomes log(12)/log(7) which is equal to 1.276989... which becomes 1.2770 rounded to 4 decimal places.
logb(5b^4) becomes log7(5*7^4) which becomes log7(5*2401) which becomes log7(12005) which becomes log(12005)/log(7) which is equal to 4.8270874...which becomes 4.8271 rounded to 4 decimal places.
logb ^8sqrt(3b) ?????
i'm not exactly sure what to do with this.
did you mean logb(8*sqrt(3b)), or did you mean:
logb^8(sqrt(3b)) ?????
what is the base?
what is the argument of the log?
in logb(x), b is the base, and x is the argument of the log.
if you can't do that, then give it in english, such as log of (sqrt(3b)) to the base of b.
as it stand, i just can't figure it out.
Answer by MathTherapy(10552)  (Show Source):
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