Question

If 5 - log10 root 1 + x + 4 log10 root 1-x = log10 1/ 1-x2, then 100 x equals

Answer 1

5 - log10 $\sqrt{1+x}+4\,log_{10}\sqrt1-x=\,log_{10}\frac{1}{\sqrt1-x^2}$
5 - log10 $\sqrt{1+x}+4\,log_{10}\sqrt1-x=\,log_{10}(\frac{1}{\sqrt1-x^2}\frac{1}{\sqrt1-x})$
5 log10 $\sqrt{1+x}+4\,log_{10}\sqrt1-x=\,log_{10}\sqrt1-x=-log\sqrt1-x.log_{10}\sqrt{1+x}$
4 log10 $\sqrt{1-x}+\,log_{10}\sqrt1-x=-5$

log10 $\sqrt{1-x}=-1$

$\sqrt{1-x=\frac{1}{10}}$
100x = 99.
Therefore the answer should be 99.