Question

Evaluate each of the following in terms of x and y, if it is given x = log₂3 and y = log₂5.

i) log₂15

ii) log₂7.5

iii) log₂60

iv) log₂6750

Answer 1

i) log₂15 

= log₂3 × 5 

= log₂3 + log₂5   [∵ log mn = log m + log n] 

= x + y

ii) log₂7.5

iii) log₂60

= log₂2²× 3 × 5 

= log₂2²+ log₂3 + log₂5 

= 2 log₂2 + x + y 

= 2 + x + y

iv) log₂6750

log₂6750 

= log₂2 × 3³× 5³ 

= log₂2 + log₂33 + log₂5³ 

= 1 + 3 log₂3 + 3 log₂5 

= 1 + 3x + 3y