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anonymous

  • one year ago

Express the following in terms of log x. log x^3/2 + log cube root of x I don't know how to solve this, please help!

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  1. anonymous
    • one year ago
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    \[\log x ^{\frac{ 3 }{ 2 }} + \log \sqrt[3]{x}\]

  2. anonymous
    • one year ago
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    another one i am stuck on: \[3 \log x + \log x ^{3}\]

  3. Nnesha
    • one year ago
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    familiar with the log rules ?

  4. Nnesha
    • one year ago
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    quotient rule\[\large\rm log_b x - \log_b y = \log_b \frac{ x }{ y}\] to condense you can change subtraction to division product rule \[\large\rm log_b x + \log_b y = \log_b( x \times y )\] addition ----> multiplication power rule \[\large\rm log_b x^y = y \log_b x\]

  5. Nnesha
    • one year ago
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    \(\color{blue}{\text{Originally Posted by}}\) @Zas \[\log x ^{\frac{ 3 }{ 2 }} + \log \sqrt[3]{x}\] \(\color{blue}{\text{End of Quote}}\) there is plus sign so which rule would you apply ?

  6. anonymous
    • one year ago
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    So you would multiply them?

  7. Jhannybean
    • one year ago
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    use the multiplication rule: \(\sf \log(a) + \log(b) = \log(a\cdot b)\) First start by changing \(\sf \log\sqrt[3]{x}\) into a cubic power. : \(\sf \log(x)^{1/3}\) Now apply multiplication property: \(\log(x)^{3/2} + \log(x)^{1/3} = \log(x^{3/2} \cdot x^{1/3}) =\log(x^{3/2 +1/3})\)

  8. Jhannybean
    • one year ago
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    What is \(\dfrac{3}{2} +\dfrac{1}{3}\) ?

  9. anonymous
    • one year ago
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    11/6, thank you so much!

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