Question

2logx+3logy-5logZ find the value of this.
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Answer 1

$\underline{\textsf{Given:}}$

$\mathsf{2\,logx+3\,logy-5\,logz}$

$\underline{\textsf{To find:}}$

$\textsf{Simplified form of the given expression}$

$\underline{\textsf{Solution:}}$

$\textsf{Consider,}$

$\mathsf{2\,logx+3\,logy-5\,logz}$

$\textsf{Using}$

$\boxed{\mathsf{\log\,M^n=n\,\log\,M}}$

$\mathsf{=logx^2+logy^3-logz^5}$

$\textsf{Using}$

$\boxed{\mathsf{\log\,M+\log\,N=\log\,MN}}$

$\mathsf{=log(x^2y^3)-logz^5}$

$\textsf{Using}$

$\boxed{\mathsf{\log\,M-\log\,N=\log\dfrac{M}{N}}}$

$\mathsf{=\log(\dfrac{x^2y^3}{z^5})}$

$\underline{\textsf{Answer:}}$

$\textsf{Simplified form of the given expression is}$

$\mathsf{\log(\dfrac{x^2y^3}{z^5})}$

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