Question

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ILLUSTRATION 8. Given log 2 = 0.3010 and log 3 = 0.4771, find the log of the
product of 200 and 30.
log 2 = 0.3010, and log 3 = 0.4771​

Answer 1

Step-by-step explanation:

we know log (a * b) = log( a+b)

take a = 200 and b = 30

so

log (200 * 30) = log 200 + log 30 ------------ (1)

let's solve log 200

log 200

= log ( 2 * 100)

= log ( 2 ) + log (100)

= log ( 2 ) + log (10 * 10)

= log ( 2 ) + log 10 + log 10

= 0.3010 + 1 + 1

= 2.3010

let's solve log 30

log 30

= log (3 * 10)

= log 3 + log 10

= 0.4772 + 1

= 1.4771

putting values of log 200 and log 30 in equation (1)

we have

log (200 * 30) = 2.3010 + 1.4771

= 3.7781 ans.