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).