Question

Given that log 2  0.3010 and log 7  0.8451 , find the following

(a) log 49 (b) log 560

Answer 1

Answer:

Here is the solution for your problem in the image

Answer 2

$Given \: log \: 2= 0.3010, \: log \: 5 = 0.6989$

$and \: log \: 7 = 0.8451$

$\red {a) Value \: of \: log \: 49 }$

$= log \: 7^{2}$

$= 2 log \: 7$

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

$= 2 \times 0.8451$

$\green { = 1.6902}$

$\therefore \red {Value \: of \: log \: 49 }\green { = 1.6902}$

$\red{ b) Value \: of \: log \: 560 }$

$= log \: ( 2^{4} \times 5 \times 7 )$

$= log \: 2^{4} + log \:5 + log \: 7$

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

$= 4 log \: 2 + log \:5 + log \: 7$

$= 4 \times 0.3010 + 0.6989 + 0.8451$

$= 1.2040 + 0.6989 + 0.8451$

$= 2.748$

$\therefore \red{ Value \: of \: log \: 560 }\green { = 2.748 }$

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