how would i condense this...
3lnxy-2ln2y. whenever i condense i get ln(xy^3/2y2).
but my teacher has ln(x^3y/4).
can someone please show me how to get that answer thanks!
3lnxy-2ln2y
= ln(x^3y^3) - ln(4y^2
= ln [(x^3y^3)/(4y^2)]
= ln [(x^3y)/4]
ahhhaaa....thanks:)
To condense the expression 3ln(xy) - 2ln(2y), we can use the following steps:
Step 1: Apply the logarithmic property ln(a) - ln(b) = ln(a/b) to simplify the expression.
3ln(xy) - 2ln(2y) = ln((xy)^3) - ln((2y)^2)
Step 2: Simplify the exponents inside the logarithms.
ln((xy)^3) - ln((2y)^2) = ln(x^3y^3) - ln(4y^2)
Step 3: Apply the logarithmic property ln(ab) = ln(a) + ln(b) to separate the terms.
ln(x^3y^3) - ln(4y^2) = ln(x^3) + ln(y^3) - ln(4) - ln(y^2)
Step 4: Simplify the expressions separately.
ln(x^3) + ln(y^3) - ln(4) - ln(y^2) = ln(x^3) + ln(y^3/y^2) - ln(4)
= ln(x^3) + ln(y) - ln(4)
Step 5: Combine the terms with addition/subtraction into a single logarithm using the logarithmic property.
ln(x^3) + ln(y) - ln(4) = ln(x^3y) - ln(4)
Therefore, the condensed form of the expression 3ln(xy) - 2ln(2y) is ln(x^3y) - ln(4).