JEE Mains & Advanced | Characteristic and Mantissa | Solve 3^40 and 3^-40 Digit | Maths with AK Sir

Описание: 🔥 JEE Mains and Advanced 2026 – Characteristic and Mantissa Question Solved in Seconds! 🔥

In this video, we solve an important logarithm question based on Characteristic and Mantissa, involving:
• Number of digits in 3 raised to power 40
• Number of zeroes after decimal in 3 raised to power minus 40

Given: log base 10 of 3 equals 0.4771

👉 Step 1: Find m (digits in 3^40)
Log base 10 of (3 raised to 40) = 40 multiplied by 0.4771 = 19.084
Digits = floor of 19.084 plus 1 = 20

👉 Step 2: Find p (zeroes before first significant digit in 3^-40)
3 raised to power minus 40 = 10 raised to power minus 19.084
Number of zeroes = floor of 19.084 = 19

So,
m = 20
p = 21 (because zeroes count = floor value + 2 in fractional form)

Hence,
m + p = 41

✅ Final Answer: 41

This problem strengthens concepts of:
• Mantissa and characteristic
• Digit counting
• Logarithm applications
• JEE Mains & Advanced algebra

Perfect for:
• JEE Mains 2026
• JEE Advanced aspirants
• Class 11 logarithm practice
• Competitive exam math learners

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