If log _{10} 2 = 0.3010 and log _{10} 7 = 0.8 | vedclass

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(A) We are given $\log _{10} 2 = 0.3010$ and $\log _{10} 7 = 0.8451$.We need to find the value of $\log _{10} 2.8$.$\log _{10} 2.8 = \log _{10} \left(

Vedclass · Accepted Answer

$0.4471$

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(A) We are given $\log _{10} 2 = 0.3010$ and $\log _{10} 7 = 0.8451$.We need to find the value of $\log _{10} 2.8$.$\log _{10} 2.8 = \log _{10} \left( \frac{28}{10} ight) = \log _{10} \left( \frac{2^2 	imes 7}{10} ight)$.Using the properties of logarithms,$\log(a 	imes b) = \log a + \log b$,$\log(a/b) = \log a - \log b$,and $\log(a^n) = n \log a$:$\log _{10} 2.8 = \log _{10} (2^2) + \log _{10} 7 - \log _{10} 10$.$= 2 \log _{10} 2 + \log _{10} 7 - 1$.$= 2(0.3010) + 0.8451 - 1$.$= 0.6020 + 0.8451 - 1$.$= 1.4471 - 1 = 0.4471$.

If $\log _{10} 2 = 0.3010$ and $\log _{10} 7 = 0.8451,$ then the value of $\log _{10} 2.8$ is

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