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# Log (base 2) 192 is equivalent to which statement(s): a)  log (base 2) 64 x log (base...

kristenmarieb... | Student, Grade 10 | Valedictorian

Posted August 15, 2013 at 5:48 PM via web

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Log (base 2) 192 is equivalent to which statement(s):

a)  log (base 2) 64 x log (base 2) 3 = 6log (base 2) 3

b)  log (base 2) 64 + log (base 2) 3 = 6 + log (base 2) 3

c)  log (base 2) 32 x log (base 2) 6 = 5log (base 2) 6

d)  log (base 2) 32 + log (base 2) 6 = 5 + log (base 2) 6

e)  log (bas 2) 8 x log (base 2) 24 = 3log (base 2) 24

f)  log (base 2) 8 + log (base 2) 24 = 3 + log (base 2) 24

If there are multiple answers, separate each with a comma.

Tagged with algebra2, math

llltkl | College Teacher | Valedictorian

Posted August 15, 2013 at 6:22 PM (Answer #1)

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`log_2(192)=log_2(64*3)`

`=log_2(64)+log_2(3)`         (using `log_a(m*n)=log_am+log_an` )

`=log_2(2^6)+log_2(3)`

`=6log_2(2)+log_2(3)`        (using `log_am^n` =`nlog_am` )

`=6+log_2(3)`

Again, `log_2(192)=log_2(32*6)`

`=log_2(32)+log_2(6)`

`=log_2(2^5)+log_2(6)`

`=5log_2(2)+log_2(6)`

`=5+log_2(6)`

We can also write `log_2(192)=log_2(8*24)`

`=log_2(8)+log_2(24)`

`=log_2(2^3)+log_2(24)`

`=3log_2(2)+log_2(24)`

`=3+log_2(24)`

Therefore, the correct options are b), d) and f).

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