Question

Choose the correct option:
If log5 = 0.69897. find the value of log500.
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Answer 1

Answer:

hope it will be helpful

Answer 2

$Given \: log \: 5 = 0.69897 \: ---(1)$

$\red{ The \: value\: of \: log \: 500 } \\= log \: ( 5 \times 100 ) \\= log \: 5 + log \: 100$

$\boxed{ \pink{ \because log \: (mn ) = log \: m + log \: n }}$

$= log \: 5 + log \: 10^{2}$

$= log \: 5 + 2 \times log \: 10$

$\boxed{ \blue{ \because log \: a^{m} = m log \: a }}$

$= log \: 5 + 2 \times 1$

$\boxed{ \blue{ \because log_{10} 10 = 1 }}$

$= 0.69897 + 2 \: [ From \: (1) ]$

$= 2.69897$

Therefore.,

$\red{ The \: value\: of \: log \: 500 }\green { = 2.69897}$

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