Answered

Find the best answers to your questions at Westonci.ca, where experts and enthusiasts provide accurate, reliable information. Experience the ease of finding quick and accurate answers to your questions from professionals on our platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

What is 2 log Subscript 5 Baseline (5 x cubed) one-third log Subscript 5 Baseline (x squared 6) written as a single logarithm? log Subscript 5 Baseline (25 x Superscript 5 Baseline) RootIndex 3 StartRoot x squared 6 EndRot log Subscript 5 Baseline (25 x Superscript 6 Baseline) RootIndex 3 StartRoot x squared 6 EndRoot log Subscript 5 Baseline 25 x Superscript 5 Baseline log Subscript 5 Baseline 2 log one-third x squared (log Subscript 5 Baseline 25 log Subscript 5 Baseline Superscript 6 Baseline) (log Subscript 5 Baseline RootIndex 3 StartRoot x squared 6 EndRoot).

Sagot :

The solution of the logarithms equation is [tex]\rm log_5(25x^6\sqrt[3]{x^2+6}})[/tex]

Given

The following expression:

[tex]\rm 2log_5(5x^3)+\dfrac{1}{3}log_5(x^2+6)[/tex]

What properties for Logarithms are used to solve the equation?

The following properties are used in the logarithms equation given below.

[tex]\rm loga+logb=logab\\\\ loga-logb=log(\dfrac{a}{b})\\\\ loga^n=nloga[/tex]

According to the Power of a power property:

  • Step 1: Apply the third property for logarithms shown above:

                   [tex]\rm 2log_5(5x^3)+\dfrac{1}{3}log_5(x^2+6)\\\\\rm log_5(5x^3)^2+\log_5(x^2+6)^{\frac{1}{3}}[/tex]

  • Step 2: Apply the Power of a power property:

                     [tex]\rm log_5(5x^3)^2+\log_5(x^2+6)^{\frac{1}{3}}\\\\log_5(25x^6)+log_5(\sqrt[3]{x^2+6}})[/tex]

  • Step 3: Using the property for Radicals;

                     [tex]\rm log_5(25x^6)+log_5(\sqrt[3]{x^2+6}})\\\\ log_5(25x^6\sqrt[3]{x^2+6}})[/tex]

Hence, the solution of the logarithms equation is [tex]\rm log_5(25x^6\sqrt[3]{x^2+6}})[/tex].

To know more about logarithms properties click the link given below.

https://brainly.com/question/26053315

M8REBEL

Answer:

The correct Answer is B

Step-by-step explanation:

Correct on Edge

We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.