Question
Prove that $\log _{10} 125=3\left(1-\log _{10} 2\right)$
✓
Answer
$\text { L.H.S. }$
$=\log _{10} 125$
$=\log _{10}\left(\frac{1000}{8}\right)$
$=\log _{10} 1000-\log _{10} 8$
$=\log _{10}(10)^3-\log _{10}(2)^3$
$=3 \log _{10} 10-3 \log _{10} 2$
$=3 \times 1-3 \log _{10} 2$
$=3\left(1-\log _{10} 2\right)$
$=\text { R.H.S. }$
$=\log _{10} 125$
$=\log _{10}\left(\frac{1000}{8}\right)$
$=\log _{10} 1000-\log _{10} 8$
$=\log _{10}(10)^3-\log _{10}(2)^3$
$=3 \log _{10} 10-3 \log _{10} 2$
$=3 \times 1-3 \log _{10} 2$
$=3\left(1-\log _{10} 2\right)$
$=\text { R.H.S. }$
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