Question 999566: given that log 3 = 301 and log 2 = 0.477. find log (tan60)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i think you got your numbers mixed up.
log(2) = .301
log(3) = .477
you want to find log(tan(60))
tan(60) = sqrt(3).
this is derived from the 30-60-90 triangle where sin(60) = sqrt(3) / 2 and cos(60) = 1/2.
tan(60) = sin(60) / cos(60) = (sqrt(3)/2) / (1/2) which results in tan(60) being equal to sqrt(3).
if you want log(tan(60)), then you need to get log(sqrt(3)).
log(sqrt(3)) is equivalent to log(3^(1/2)) which is equivalent to 1/2 * log(3).
since log(3) is equal to .477, then log(sqrt(3)) = 1/2 * .477 = .2385
if you use your calculator, you will see that log(sqrt(3)) is equal to .2385606274.
the difference is due to rounding.
you did not need log(2) = .301 because the problem did not require you to use log(2) in any way.
IF the problem wanted you to find log(sin(60)), then log(2) would have come into play.
in that case, sin(60) = sqrt(3)/2, so log(sin(60)) would need to find log(sqrt(3)/2).
that would then be equivalent to log(sqrt(3)) - log(2), which would then be equivalent to 1/2 * log(3) - log(2), which would then result in .2385 - .301 = -.0625.
if you use you calculator to find log(sqrt(3)/2), your calculator will tell you that the answer is -.0624693683.
that's pretty close to -.0625 with the difference due to rounding.
why rounding errors?
because log(3) = .4771212547 and log(2) = .3010299957
.477 and .301 are rounded versions of the more detailed values for each.
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