What is the answer for question 5) ?

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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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