Question 1148108
you are given:


log(5) = a
log(3) = b
log(2) = c


you want to find log_30(8).
you can use the log base conversion formula to get:
log_30(8) = log(8) / log(30)


we start with log_30(8) = log(8) / log(30).
8 is equal to 2^3 and 30 is equal to 5 * 3 * 2, so the formula becomes:
log_30(8) = log(2^3) / log(5 * 3 * 2)
by the rules of logarithms, this becomes:
log_30(8) = 3 * log(2) / (log(5) + log(3) + log(2))
since log(5) = a and log(3) = b and log(2) = c, we get:
log_30(8) = (3 * c) / (a + b + c)


your answer should be:


log_30(8) = (3 * c) / (a + b + c)


to see if that's true, we replace a, b, c with their respective values of:
a = log(5)
b = log(3)
c = log(2)
to get:
log_30(8) = 3 * log(2) / (log(5) + log(3) + log(2)) = .6113851413.


you can use your calculator to see that log(8) / log(30) = the same value.


you can also use your calculator to see that log_30(8) = .6113851413 if and only if 30 ^ .6113851413 = 8.
it did equal that on my calculator.