Question
If $ \log_{10} 8 = 0.90;$ find the value of : $\log\sqrt{32}$
✓
Answer
Given that $\log _{10} 8=0.90$
$ \Rightarrow \log _{10} 2 \times 2 \times 2=0.90$
$ \Rightarrow \log _{10} 2^3=0.90$
$ \Rightarrow 3 \log _{10} 2=0.90$
$ \Rightarrow \log _{10} 2=\frac{0.90}{3}$
$\Rightarrow \log _{10} 2=0.30\ldots(1)$
$ \log \sqrt{32}$
$ =\log _{10}(32)^{\frac{1}{2}}$
$ =\frac{1}{2} \log _{10}(32)$
$ =\frac{1}{2} \log _{10}(2 \times 2 \times 2 \times 2 \times 2)$
$ =\frac{1}{2} \log _{10}\left(2^5\right)$
$ =\frac{1}{2} \times 5 \log _{10} 2$
$=\frac{1}{2} \times 5(0.30)$
$[$from$(1)]$
$ =5 \times 0.15$
$ =0.75$
$ \Rightarrow \log _{10} 2 \times 2 \times 2=0.90$
$ \Rightarrow \log _{10} 2^3=0.90$
$ \Rightarrow 3 \log _{10} 2=0.90$
$ \Rightarrow \log _{10} 2=\frac{0.90}{3}$
$\Rightarrow \log _{10} 2=0.30\ldots(1)$
$ \log \sqrt{32}$
$ =\log _{10}(32)^{\frac{1}{2}}$
$ =\frac{1}{2} \log _{10}(32)$
$ =\frac{1}{2} \log _{10}(2 \times 2 \times 2 \times 2 \times 2)$
$ =\frac{1}{2} \log _{10}\left(2^5\right)$
$ =\frac{1}{2} \times 5 \log _{10} 2$
$=\frac{1}{2} \times 5(0.30)$
$[$from$(1)]$
$ =5 \times 0.15$
$ =0.75$
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