Condense the expression: 1/5log3(32) - 2log3x + 1/2log3y
I can't put the 3 as a small number on the bottom on all 3 parts of the trinomial.
To condense the expression 1/5log3(32) - 2log3x + 1/2log3y, we need to combine the logarithmic terms that have the same base.
Let's break down each term separately:
1/5log3(32):
This term can be condensed by simplifying the logarithm of 32 base 3. We can rewrite 32 as a power of 3 to get:
32 = 3^5
Therefore, 1/5log3(32) = 1/5log3(3^5). According to the rule of logarithms, this can be simplified to:
1/5(5) = 1
-2log3x:
This term doesn't have any logs with the same base to combine with. Hence, we keep it as it is.
1/2log3y:
Similar to the previous term, there are no other log terms with the base 3 to combine with. We keep it as it is.
Combining all three terms, we get:
1 - 2log3x + 1/2log3y