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Write the following as a sum of logarithms: log(x^(9)y^(2)z^(2))= ◻ log(x)+ ◻ log(y)+ ◻ log(z) Nextitem

1717.\newlineWrite the following as a sum of logarithms:\newlinelog⁡(x9y2z2)= \log \left(x^{9} y^{2} z^{2}\right)= \newline□ \square log⁡(x)+ \log (x)+ □ \square log⁡(y)+ \log (y)+ □ \square log⁡(z) \log (z) \newlineNextitem

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Q. 1717.\newlineWrite the following as a sum of logarithms:\newlinelog⁡(x9y2z2)= \log \left(x^{9} y^{2} z^{2}\right)= \newline□ \square log⁡(x)+ \log (x)+ □ \square log⁡(y)+ \log (y)+ □ \square log⁡(z) \log (z) \newlineNextitem
  1. Split expression: Using the logarithmic identity log⁡(a∗b)=log⁡(a)+log⁡(b)\log(a*b) = \log(a) + \log(b), split the expression:\newlinelog⁡(x9y2z2)=log⁡(x9)+log⁡(y2)+log⁡(z2)\log(x^{9}y^{2}z^{2}) = \log(x^{9}) + \log(y^{2}) + \log(z^{2})
  2. Apply power rule: Apply the power rule of logarithms, log⁡(ab)=blog⁡(a)\log(a^b) = b\log(a), to each term:\newlinelog⁡(x9)=9log⁡(x)\log(x^{9}) = 9\log(x), log⁡(y2)=2log⁡(y)\log(y^{2}) = 2\log(y), log⁡(z2)=2log⁡(z)\log(z^{2}) = 2\log(z)
  3. Combine results: Combine the results from the previous step: log⁡(x9y2z2)=9log⁡(x)+2log⁡(y)+2log⁡(z)\log(x^{9}y^{2}z^{2}) = 9\log(x) + 2\log(y) + 2\log(z)

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