To simplify this expression, we can use the properties of logarithms:
Log3(5√3) - log3(5)
Using the property that log(a) - log(b) = log(a/b), we can combine the two logarithms:
= log3((5√3)/5)
= log3(√3)
Since √3 can be simplified as 3^(1/2), we have:
= log3(3^(1/2))
Using the property log(a^b) = b*log(a), we can simplify further:
= (1/2)log3(3)
Since log3(3) = 1, the expression simplifies to:
= 1/2
Therefore, log3(5√3) - log3(5) = 1/2.
To simplify this expression, we can use the properties of logarithms:
Log3(5√3) - log3(5)
Using the property that log(a) - log(b) = log(a/b), we can combine the two logarithms:
= log3((5√3)/5)
= log3(√3)
Since √3 can be simplified as 3^(1/2), we have:
= log3(3^(1/2))
Using the property log(a^b) = b*log(a), we can simplify further:
= (1/2)log3(3)
Since log3(3) = 1, the expression simplifies to:
= 1/2
Therefore, log3(5√3) - log3(5) = 1/2.