Question

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

Answer 1

Correct Answer: 99

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.