Question

Can you solve this exercise?
please solve so I understand

Answer 1

`= 4 - 4 \: log_(5)(10) - 4 log_(2)(10) + 4 log_(2)(10) log_(5)(10) \\ \\ or \: \\ \\ = 4`

the answer is 2

hope it helps

see the attachment for explanation

Answer 2

Answer is 2). 4

Step-by-step explanation:

`{ \rm{(2 - log_( √(2) )10)(2 - log_( √(5) )10)}}`

• let's open the brackets:

`{ \rm{(2 * 2) + (2 * - log_( √(5) )10 ) + (2 * - log_( √(2) )10) + ( log_( √(2) )10 * log_( √(5) )10) }} \\ \\ = { \rm{4 - 2 log_( √(5) )10 - 2 log_( √(2) )10 + ( log_( √(5) )10)( log_( √(2) )10)}}`

• change log√5 to log√2:

`{ \rm{4 - 2 log_( √(2) )10 - ((2 log_( √(2) )10 )/( log_( √(2) ) √(5) ) ) + ( log_( √(2) )10)( ( log_( √(2) )10 )/( log_( √(2) ) √(5) ) )}} \\ \\ = { \rm{4 - 2 log_( √(2) )10 - ( (4 log_( √(2) )10)/( log_( √(2) ) √(5) )) }} \\ \\ = { \rm{4 - 2 log_( √(2) )10 - ( (8 log_( √(2) )(5 * 2) )/( log_( √(2) )5) )}} \\ \\ = { \rm{4 - 2 log_( √(2) )(5 * 2) - (8 log_( √(2) )2)/( log_( √(2) )5 ) }}`

• now let's change log√2 to log10

`= { \rm{4 - (2 log_(10)10)/( log_(10) √(2) ) - (8 log_(10)2)/( log_(10) √(2) ) / ( log_(10)5 )/( log_(10) √(2) ) }} \\ \\ = { \rm{4 - (2)/(0.3) - (2.41)/(0.3) * (0.3)/(0.7) }} \\ \\ = { \rm{4 + (41)/(70) }} \\ \\ { \rm{ = 4 (41)/(70) \: \approx \: 4 }}`