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If ` ` `log_4 3` is approximately .7925, evaluate `log_4 (1/9)` .  Give your answer...

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kristenmarieb... | Student, Grade 10 | Valedictorian

Posted August 15, 2013 at 7:57 PM via web

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If ` ` `log_4 3` is approximately .7925, evaluate `log_4 (1/9)` .  Give your answer to four decimals.  

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mvcdc | Student , Undergraduate | (Level 1) Associate Educator

Posted August 15, 2013 at 8:36 PM (Answer #1)

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We start by simplifying `log_4(1/9)`  and expressing it in terms of `log_4 3` .

Notice that we can express `1/9`  as `1/(3^2)`  or `3^(-2)` .

Hence, `log_4 (1/9) = log_4 3^(-2)` .

Using a property of logarithm: `log a^b = b log a` , we can express `log_4 3^(-2)` as `-2 log_4 3` .

Now, using the given value, we can simplify this to:

`-2*0.7925 = -1.5850`

Hence, 

log(base 4) (1/9) = -1.5850 

if you use a calculator, you will get: -1.58496250072... which rounds to -1.5850.

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