IPMAT Indore 2025 (MCQ) - If _25 [5 _3 (1+_3(1+2_2x))] = 12 then x is: | PYQs + Solutions | AfterBoards
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IPMAT Indore 2025

Modern Math
>
Logarithms

Easy

If log⁡25[5log⁡3(1+log⁡3(1+2log⁡2x))]=12\log_{25} [5 \log_3 (1+\log_3(1+2\log_2x))] = \frac12 then xx is:

✅ Correct Option: 2
We start by simplifying the outer logarithm:
If log⁡25(y)=12\log_{25}(y) = \frac{1}{2}, then y=2512=5y = 25^{\frac12} = 5.
5log⁡3(1+log⁡3(1+2log⁡2x))=55 \log_3 (1+\log_3(1+2\log_2x)) = 5
Dividing both sides by 5:
log⁡3(1+log⁡3(1+2log⁡2x))=1\log_3 (1+\log_3(1+2\log_2x)) = 1
Since log⁡3(3)=1\log_3(3) = 1, we have:
1+log⁡3(1+2log⁡2x)=31+\log_3(1+2\log_2x) = 3
∴log⁡3(1+2log⁡2x)=2\therefore \log_3(1+2\log_2x) = 2
Since log⁡3(9)=2\log_3(9) = 2, we have:
1+2log⁡2x=91+2\log_2x = 9
Therefore: 2log⁡2x=82\log_2x = 8
So: log⁡2x=4\log_2x = 4
log⁡2x=4\log_2x = 4 means x=24=16x = 2^4 = 16
Therefore, x=16x = 16 is our answer.
Verification: Substituting x=16x = 16 back into the original equation confirms our answer.

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