Expand the expression of log5x^(1/3)y^6
5 is the base of the log.
this is pretty tricky stuff and im not sure how to attempt it..
Tricky?
1/3 log5 x + 6log5 y
Where is the trick?
Ok well bobpursley first of all your a genius ;) second of all im a newbie at this logorithm stuff. thank you for helping me!
To expand the expression log5(x^(1/3)y^6), you need to apply the properties of logarithms. Let's break it down step by step:
Step 1: Start with the original expression: log5(x^(1/3)y^6).
Step 2: Apply the product rule of logarithms which states that log(ab) = log(a) + log(b):
log5(x^(1/3)y^6) = log5(x^(1/3)) + log5(y^6).
Step 3: Simplify each logarithm separately. Using the rule loga(x^b) = b*loga(x), we have:
log5(x^(1/3)) = (1/3) * log5(x) and log5(y^6) = 6 * log5(y).
Step 4: Substitute the simplified logarithms back into the original expression:
log5(x^(1/3)y^6) = (1/3) * log5(x) + 6 * log5(y).
That's the expanded form of the given expression log5(x^(1/3)y^6).