Evaluate: frac{log sqrt{27}+log sqrt{1000}+lo | vedclass

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Question

(C) Given expression: $\frac{\log \sqrt{27}+\log \sqrt{1000}+\log 8}{\log 120}$Step $1$: Simplify the numerator terms.$\log \sqrt{27} = \log (3^3)^{1/

Vedclass · Accepted Answer

$3/2$

Vedclass · Answer

(C) Given expression: $\frac{\log \sqrt{27}+\log \sqrt{1000}+\log 8}{\log 120}$Step $1$: Simplify the numerator terms.$\log \sqrt{27} = \log (3^3)^{1/2} = \frac{3}{2} \log 3$$\log \sqrt{1000} = \log (10^3)^{1/2} = \frac{3}{2} \log 10$$\log 8 = \log 2^3 = 3 \log 2 = \frac{3}{2} \log 2^2 = \frac{3}{2} \log 4$Step $2$: Substitute these into the numerator.Numerator $= \frac{3}{2} \log 3 + \frac{3}{2} \log 10 + \frac{3}{2} \log 4 = \frac{3}{2} (\log 3 + \log 10 + \log 4)$Step $3$: Use the property $\log a + \log b + \log c = \log (a \cdot b \cdot c)$.Numerator $= \frac{3}{2} \log (3 \cdot 10 \cdot 4) = \frac{3}{2} \log 120$Step $4$: Divide by the denominator.$\frac{\frac{3}{2} \log 120}{\log 120} = \frac{3}{2}$

Evaluate: $\frac{\log \sqrt{27}+\log \sqrt{1000}+\log 8}{\log 120}$

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