Given:

log(10,5)=a, log(10,3)=b, log(10,2)=c

Find: log(30,8)

not familiar with your notation

does log(30,8) mean log30 8 ?

log(30,8) = log8/log30

Since the base on the right does not matter, we can use base 10, giving us

3log2/(log2+log3+log5)
= 3c/(c+b+a)

Yes

Thanks Steve

To find the value of log(30,8), we will use the Change of Base Formula, which states that:

log(base a, x) = log(base b, x) / log(base b, a)

In this case, we want to find log(30,8), but we only have logarithms with base 10. So, we need to express log(30,8) in terms of base 10 logarithms.

First, let's express 30 as a product of the numbers we have logarithms for: 30 = 2 * 3 * 5.

Now, let's use the Change of Base Formula to express log(30,8) in terms of base 10 logarithms:

log(30,8) = log(10,8) / log(10,30)

Since we know the values of a, b, and c, we can substitute them into the formula:

log(30,8) = log(10,8) / log(10,30) = c^3 / (a + b + c)

Therefore, log(30,8) is equal to c^3 / (a + b + c).