Question

Evaluate each of the following in terms of x and y if it is given that x=log 3base2 and y=log 5base2
A) log 15base2
B) log 7.5 base2
C)log 60 base 2
D) log 6750base 2

Answer 1

hello users ......

we have given that :
$x = log_{2}3$
and
$y = log_{2} 5$

we have to find :-
A . $log_{2} 15 = ?$
B .  $log_{2} 7.5= ?$
C .  $log_{2} 60 = ?$
D .  $log_{2} 6750 = ?$

solution :-
A . $log_{2} 15 =$ 
=  $log_{2} 3 * 5$
=   $log_{2} 3$  +  $log_{2} 5$ 
= x + y answer 

B .  $log_{2} 7.5$
= $log_{2} 75 / 10$
= $log_{2} 75$ - $log_{2} 10$
= $log_{2} 25 * 3$  - $log_{2} 5 * 2$
= [ $log_{2}5²$ + $log_{2}3$ ] - [ $log_{2} 5$ + $log_{2} 2$ ]
=2  $log_{2} 5$ +  $log_{2}3$ -  $log_{2} 5$ - 1
=  $log_{2} 5$ -  $log_{2} 3$ - 1
= y - x - 1 answer 

C .  $log_{2} 60$
= $log_{2} 15 * 4$ 
= $log_{2} 15$ + $log_{2} 4$
= $log_{2} 3*5$ + $log_{2}2²$
= $log_{2} 3$ + $log_{2} 5$ + 2 $log_{2} 2$
= $log_{2}3$ + $log_{2}5$ + 2
= x + y + 2 answer 

D .  $log_{2} 6750$
= $log_{2} 125*27*2$
=$log_{2}125$ + $log_{2}27$ + $log_{2} 2$
= $log_{2} 5³$ + $log_{2} 3³$ + 1
= 3$log_{2}5$ + 3$log_{2} 3$ + 1
= 3y + 3x + 1 answer 

✮✮ hope it helps ✮✮

Answer 2

Step-by-step explanation:

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