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What is the answer for question 5) ? http://postimg.org/image/xusvq33e3/  

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lkballer24 | Student, Grade 11 | (Level 1) Valedictorian

Posted May 17, 2013 at 12:12 PM via web

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What is the answer for question 5) ?

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llltkl | College Teacher | (Level 3) Valedictorian

Posted May 17, 2013 at 1:00 PM (Answer #1)

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a) To find the value of `log_(8)4`

Let `log_(8)4=x`

By the definition of logarithms, that is equivalent to the exponential equation:

`4=8^(x)`

`=>2^(2)=(2^(3))^x`

Since the base 2 is same on both sides & positive and not equal to 1, we can equate the exponents:

`2=3^x`  

`rArr 2/3=x`

Hence the final answer is `log_(8)4=x=2/3`

b) To find the value of `log_(1/3)27`

Let `log_(1/3)27=x`

`rArr log_(1/3)3^3=x`

By the definition of logarithms, that is equivalent to the exponential equation:

`3^3=(1/3)^x`

` ``rArr 3^3=3^-x`

Since the base 3 is same on both sides & positive and not equal to 1, we can equate the exponents:

`rArr x=-3`

Hence the final answer is `log_(1/3)27=-3`

 

                                                                               

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