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Math  /  Algebra

QuestionFind the value. log⁡584−log⁡303log⁡584−log⁡303≈□\begin{array}{l} \log 584-\log 303 \\ \log 584-\log 303 \approx \square \end{array} □\square (Round to four decimal places as needed.)

Studdy Solution

STEP 1

What is this asking? We're asked to find the difference between the logarithm of 584 and the logarithm of 303, then round the result to four decimal places. Watch out! Remember the logarithm properties!
Also, don't forget to round your final answer correctly.

STEP 2

1. Rewrite the expression using logarithm properties.
2. Calculate the logarithm.
3. Round the result.

STEP 3

We're dealing with the *difference* of two logarithms with the same base (which is 10, since it's not explicitly written).
This screams "logarithm property"!
Remember, log⁡a−log⁡b=log⁡(ab)\log a - \log b = \log(\frac{a}{b}).
So, let's **rewrite** our expression: log⁡584−log⁡303=log⁡(584303) \log 584 - \log 303 = \log\left(\frac{584}{303}\right) This makes our calculation much easier!

STEP 4

Now, we can **calculate** the value of this single logarithm: log⁡(584303)≈log⁡(1.92739)≈0.285124 \log\left(\frac{584}{303}\right) \approx \log(1.92739) \approx \mathbf{0.285124} Remember, this is an approximation, so we keep more decimal places than needed for the final answer.

STEP 5

Finally, let's **round** our result to four decimal places, as requested: 0.285124≈0.2851 \mathbf{0.285124} \approx 0.2851 And there we have it!

STEP 6

The value of log⁡584−log⁡303\log 584 - \log 303 rounded to four decimal places is 0.2851.

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