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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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(-10) - |(-20) – (+30) |
myrzilka [38]

ANSWER: -60

EXPLANATION: To solve for (-10) - |(-20) – (+30) |, we need to do:

−10−| −20 − 30|, which equals −10−|−50|. Next, we do −10−50, which is -60.

−10−|−20−30|

= −10−|−50|

= −10−50

= −60

6 0
2 years ago
Emily buys a toaster for 10%off if she pays 36 then what was the original price
PtichkaEL [24]
x-0.1x=36

where x is the original price
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36 is the price paid

x-0.1x=36
0.9x=36
-----   ----
0.9     0.9
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The original price is $40.00

7 0
3 years ago
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Step-by-step explanation:

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