Question

(Log(base 2) 10).(log(base2) 80)-(log(base2) 5).(log(base2) 160)

Answer 1

Answer:

(log₂10).(log₂80) - (log₂5).(log₂160) = 4

Step-by-step explanation:

(Log(base 2) 10).(log(base2) 80)-(log(base2) 5).(log(base2) 160)

(log₂10).(log₂80) - (log₂5).(log₂160)

80 = 8 * 10 = 2³*10

5 = 10/2  = 10 *2⁻¹

160 = 16 * 19 = 2⁴*10

=(log₂10).(log₂2³*10) - (log₂10*2⁻¹).(log₂2⁴*10)

logₓ(ab) = logₓa + logₓb

logₓ(xⁿ)  = n

= (log₂10).( 3 + log₂10)  -  (log₂10 - 1).(4  + log₂10)

= (log₂10)² + 3log₂10  - ( (log₂10)² + 3log₂10 - 4)

= (log₂10)² + 3log₂10  - (log₂10)² - 3log₂10 + 4

= 4

(log₂10).(log₂80) - (log₂5).(log₂160) = 4