Question

[log9√3√3√3] log10 0.01= ?​

Answer 1

$\underline{\textbf{Given:}}$

$\mathsf{(log_9\sqrt{3}\sqrt{3}\sqrt{3}){\times}log_{10}0.01}$

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

$\textsf{The value of}$

$\mathsf{(log_9\sqrt{3}\sqrt{3}\sqrt{3}){\times}log_{10}0.01}$

$\underline{\textbf{Solution:}}$

$\mathsf{Consider,}$

$\mathsf{(log_9\sqrt{3}\sqrt{3}\sqrt{3}){\times}log_{10}0.01}$

$\mathsf{=(log_93\sqrt{3}){\times}log_{10}\left(\dfrac{1}{100}\right)}$

$\mathsf{=(log_99^\frac{1}{2}9^\frac{1}{4}){\times}log_{10}\left(\dfrac{1}{10^2}\right)}$

$\mathsf{=(log_99^\frac{1}{2}+log_99^\frac{1}{4}){\times}log_{10}10^{-2}}$

$\mathsf{Using,}$

$\boxed{\mathsf{log_aM^n=n\;log_aM}}$

$\mathsf{=\left(\dfrac{1}{2}log_99+\dfrac{1}{4}log_99\right){\times}(-2\,log_{10}10)}$

$\mathsf{=\left(\dfrac{1}{2}(1)+\dfrac{1}{4}(1)\right){\times}(-2(1))}$

$\mathsf{=\left(\dfrac{1}{2}(1)+\dfrac{1}{4}(1)\right){\times}(-2(1))}$

$\mathsf{=\dfrac{3}{4}{\times}(-2)}$

$\mathsf{=\dfrac{-3}{2}}$

$\underline{\textbf{Find more:}}$

Expand log 243 to the base 3 root 3

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The value of log 0.001 to the base 0.1 is

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