Question

expand the log x3y3z4​

Answer 1

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\log \sqrt{x^2y^3y^4}

= \log \sqrt{x^2y^{3+4}} (using formula x^m*x^n=x^{m+n} )

= \log \sqrt{x^2y^7}

simplify radical

= \log (xy^3\sqrt{y})

= \log (xy^3y^{\frac{1}{2}})

(because square root is same as exponent 1/2)

Now apply formula log(mn)=log(m)+log(n)

= \log (x) + \log (y^3) + \log (y^{\frac{1}{2}})

Apply formula \log(x^m)=m \log(x)

= \log (x) + \log (y^3) + \log (y^{\frac{1}{2}})

= \log (x) +3 \log (y) + \frac{1}{2} \log (y)

= \log (x) + \frac{7}{2} \log (y)

Hence final answer is \log (x) +\frac{7}{2} \log (y)