Question 955318
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.