CAT 2024 Logarithms Question (Medium)

Question

If is a positive real number such that , then the greatest integer not exceeding , is

Accepted Answer

Step 1 We are given the equation Our goal is to simplify all logarithmic terms to base 10. Step 2 Use base conversion Substitute back into the equation Step 3 Now simplify each term - - - Add them Combine Step 4 Solve for Now, convert back to Step 5 The greatest integer not exceeding is Final Answer

CAT 2024

Quantitative

Logarithms

Medium

If $x$ is a positive real number such that $4 \log _{10} x+4 \log _{100} x+8 \log _{1000} x=13$ , then the greatest integer not exceeding $x$ , is

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