Question 955318: Please sort these out?(which has the most value , which has the lowest value)
*log2(3)* *log3(5)* *log5(8)*
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the easiest way to sort this out is to use the log base conversion formula of:
logb(a) = log10(a)/log10(b) = LOG(a)/LOG(b), where LOG is the log function of your calculator.
using this formula, you get:
log2(3) = LOG(3)/LOG(2) = 1.58496...
log3(5) = LOG(5)/LOG(3) = 1.46973...
log5(8) = LOG(8)/LOG(5) = 1.29202...
the one that has the lowest value is the last one.
you can double check your figures by using the exponential form of the logarithmic equation.
log2(3) = y if and only if 3 = 2^y
when y = 1.58496..., 2^y = 3, so we're good there.
log3(5) = y if and only if 5 = 3^y
when y = 1.46973..., 3^y = 5, so we're good there.
log5(8) = y if and only if 8 = 5^y
when y = 1.29202..., 5^y = 8, so we're good there.
log5(8) = 1.29202 gives you the smallest value of y.
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