Math, asked by pushpasharma83339, 10 months ago


If
log2=0.300 and log3=0.4771
find the value of log72?

Answers

Answered by Anonymous
6

Answer :

The value of log72 is 1.8572

Given :

  • log 2 = 0.3010
  • log 3 = 0.4771

To Find :

  • The value of log72

Formula to be used :

  •  \sf \log(ab) =  \log(a) +  \log(b)
  •   \sf\log({a}^{n} ) = n \log(a)

Solution :

 \sf \log(72) =  \log(9 \times 8) \\  \\  \sf \implies \log(72) =  \log(9) +  \log(8) \\  \\  \sf \implies \log(72) =  \log {3}^{2}  +  \log {2}^{3}  \\  \\  \sf \implies \log(72) = 2 \times  \log(3) + 3 \times  \log(2) \\  \\  \sf \implies \log(72) = 2 \times 0.4771 + 3 \times 0.3010 \\  \\  \sf \implies \log(72) = 0.9542 + 0.9030 \\  \\  \bf  \implies\log(72) = 1.8572

____________________

Definition of Logarithm :

  • If aⁿ = m , where a , n and m are real numbers , a>0 , a≠1 , then the index n is called the logarithm of the number m with respect to the base a
  • Symbolically it is given by : -
  • \sf{n=\log_{a}(m) }

Some More Logarithmic identities :

  • \sf{\log(\dfrac{a}{b}) = \log(a) - \log(b)}
  • \sf{\log_{a^{n}}(b)^{m}= \dfrac{m}{n}\log_{a}(b)}
Answered by CᴀɴᴅʏCʀᴜsʜ
0

Answer:

log(72) = log(9×8)

log(72) = log(9) +log (8)

=> log(72) = log3^2 + log2^3

=> log(72) = 2 × log(3) + 3 × log(2)

=> log(72) = 2 × 0.4771 + 3 × 0.3010

=> log(72) = 0.9542 + 0.9030

=> log(72) = 1.8572

Hope it helps you...

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