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hammer [34]
3 years ago
14

Expand the following logarithm: log of the square root of xy divided by 1000

Mathematics
1 answer:
Marysya12 [62]3 years ago
4 0
Remove parentheses<span> in </span>numerator<span>.
</span><span>1(log(<span>1/1000</span>x<span>y^2</span>))

</span>The logarithm<span> of a </span>product<span> is equal to the </span>sum<span> of the </span>logarithms<span> of each </span>factor <span>(e.g.</span><span><span>log(xy)=log(x)+log(y)</span>).</span><span> The </span>logarithm<span> of a </span>division<span> is equal to the </span>difference<span> of the </span>logarithms<span> of each </span>factor <span>(e.g.</span><span><span>log(<span>x/y</span>)=log(x)−log(y)</span>).
</span><span>1(log(x)+log(<span>y^2</span>)−log(1000))

</span>The exponent<span> of a </span>factor<span> inside a </span>logarithm<span> can be expanded to the front of the </span>expression<span> using the third law of </span>logarithms<span>. The third law of </span>logarithms<span> states that the </span>logarithm<span> of a </span>power<span> of </span>x<span> is equal to the </span>exponent<span> of that </span>power<span> times the </span>logarithm<span> of </span>x<span>(e.g.</span><span><span>lo<span>g^b</span>(<span>x^n</span>)=nlo<span>g^b</span>(x)</span>).

</span><span>log(x)+1((2log(y)))−log(1000)

</span>Remove the extra parentheses<span> from the </span>expression <span><span>1((2log(y)))</span>.
</span><span>log(x)+2log(y)−log(1000)

</span>The logarithm base 10<span> of </span>1000<span> is </span><span>3.
</span><span>log(x)+2log(y)−((3))

</span><span>Simplify.
</span>log(x)+2log(y)−<span>3
</span>
Answer:
log(x)+2log(y)−<span>3</span>
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The question has to do with scientific notation

<h3>What is scientific notation?</h3>

Scientific notation is the expression of a number in the form a ×  10ⁿ where 1 ≤ a ≤ 10 and n is an integer.

<h3>How to simplify the expression?</h3>

Now to simplify the expression (9 × 10⁻¹³) - (6.3 × 10⁻¹⁵) both number have to have the same exponent to the power of 10.

So, re-writing, we have

(9 × 10⁻¹³) - (6.3 × 10⁻¹⁵) = (9 × 10⁻¹³) - (6.3 × 10⁻¹³ × 10⁻²)

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So the domain is equal to the set of all real numbers or <em>R</em>.

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