Answered

Welcome to Westonci.ca, the place where your questions are answered by a community of knowledgeable contributors. Ask your questions and receive detailed answers from professionals with extensive experience in various fields. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

How can we simplify this expression below into a single logarithm? 3log(x)+1/2log(4y)−log(z)

Sagot :

aklee18oo

Answer:

[tex]log(\frac{2x^3\sqrt{y} }{z} )[/tex]

Step-by-step explanation:

We can start by using the power property of logarithms to rewrite the expression. We raise the contents of the logarithm to the power of the coefficient:

[tex]log(x^3) + log([4y]^\frac{1}{2} )-log(z)\\log(x^3) + log(2\sqrt{y})-log(z)[/tex]

Now, we can use both the addition and subtraction properties of logarithms to rewrite the expression. Addition becomes multiplication while subtraction becomes division:

[tex]log(\frac{x^3*2\sqrt{y}}{z} )[/tex]

And to write it in a more proper way:

[tex]log(\frac{2x^3\sqrt{y} }{z} )[/tex]

We appreciate your time. Please revisit us for more reliable answers to any questions you may have. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.