CAT 2021 Logarithms Question (Hard)

Question

If , then equals

Accepted Answer

Step 1 Given equation 5 - log_ 10 4 log_ 10 log_ 10 --- Step 2 Expand RHS log_ 10 log_ 10 left right - log_ 10 - log_ 10 --- Step 3 Combine terms Equation becomes 5 - log_ 10 4 log_ 10 - log_ 10 - log_ 10 --- Step 4 Simplify Bring like terms together 4 log_ 10 log_ 10 -5 5 log_ 10 -5 log_ 10 -1 ---

CAT 2021

Quantitative

Logarithms

Hard

If $5 - \log_{10} \sqrt{1+x} + 4 \log_{10} \sqrt{1-x} = \log_{10} \frac{1}{\sqrt{1-x^{2}}}$ , then $100x$ equals

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