Question

answer this question ​

Answer 1

Answer:

(a) 1.8751

(b) 0.8572

(c) 1.21295

Step-by-step explanation:

(a) log 75

= log ( 3 × 25 )

= log 3 + log 25

= log 3 + log ( 100 / 4 )

= log 3 + log 100 - log 4

= log 3 + log 10² - log 2²

= log 3 + 2 log 10 - 2 log 2

= 0.4771  +  2 × 1  -  2 × 0.3010

= 0.4771 + 2 - 0.6020

= 1.8751

(b)  log 7.2

= log ( 72 / 10 )

= log 72 - log 10

= log ( 8 × 9 ) - log 10

= log 8 + log 9 - log 10

= log 2³ + log 3² - log 10

= 3 log 2 + 2 log 3 - log 10

= 3 × 0.3010  +  2 × 0.4771  -  1

= 0.9030 + 0.9542 - 1

= 0.8572

(c) log 5 + log 8 - log √6

= log ( 10 / 2 ) + log 2³ - log ( 6^(1/2) )

= log 10 - log 2 + 3 log 2 - (1/2) log 6

= log 10 + 2 log 2 - (1/2) log ( 2 × 3 )

= log 10 + 2 log 2 - (1/2) log 2 - (1/2) log 3

= 1  +  2 × 0.3010  -  (1/2) × 0.3010  -  (1/2) × 0.4771

= 1 + 0.6020 - 0.1505 - 0.23855

= 1.21295