What is 2 log Subscript 5 Baseline (5 x cubed) + one-third log Subscript 5 Baseline (x squared + 6) written as a single logarithm?

Question

What is 2 log Subscript 5 Baseline (5 x cubed) + one-third log Subscript 5 Baseline (x squared + 6) written as a single logarithm?

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Aubrey 4 weeks 2021-09-28T00:16:56+00:00 2 Answers 0

Answers ( )

    0
    2021-09-28T00:18:06+00:00

    Answer: log_5(25x^6\sqrt[3]{ x^2+6})

    Step-by-step explanation:

    Given the following expression:

    2log_5(5x^3)+\frac{|}{3}log_5(x^2+6)

    You need to remember the following properties for Logarithms:

    1.\ log(a)+log(b)=log(ab)\\\\2.\ log(a)-log(b)=log(\frac{a}{b})\\\\3.\ log(a)^n=nlog(a)

    And the following property for Radicals:

    a^{\frac{1}{n}}=\sqrt[n]{a}

    According to the Power of a power property:

    (a^m)^n=a^{mn}

    Then, you can follow these steps:

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

    =log_5(5x^3)^2+log_5(x^2+6)^{\frac{1}{3}}

    Step 2: Apply the Power of a power property:

    =log_5(25x^6)+log_5(x^2+6)^{\frac{1}{3}}

     Step 3: Using the property for Radicals shown before:

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

    Step 4: Now you must apply the first property for logarithms:

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

    0
    2021-09-28T00:18:43+00:00

    B

    Step-by-step explanation:

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