Question

If
log2=0.300 and log3=0.4771
find the value of log72?
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Answer 1

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 :

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

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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 :

• $\sf{\log(\dfrac{a}{b}) = \log(a) - \log(b)}$
• $\sf{\log_{a^{n}}(b)^{m}= \dfrac{m}{n}\log_{a}(b)}$

Answer 2

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...