Q. Expand the logarithm fully using the properties of logs. Express the final answer in terms of logx, and logy.logyx2Answer:
Identify Properties: Identify the properties used to expand log(yx2). We have a logarithm of a quotient and a power. We will use the quotient property and the power property of logarithms to expand this expression. Quotient Property: logb(QP)=logbP−logbQ Power Property: logb(Pk)=k⋅logbP
Apply Quotient Property: Apply the quotient property to the logarithm log(yx2). Using the quotient property, we can write log(yx2) as log(x2)−log(y).
Apply Power Property: Apply the power property to the logarithm log(x2). Using the power property, we can write log(x2) as 2×log(x).
Combine Results: Combine the results from Step 2 and Step 3 to get the final expanded form.The final expanded form is 2⋅log(x)−log(y).
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