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

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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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