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balu736 [363]
3 years ago
9

Express the given quantity as a single logarithm and simplify: 3logx+2log(y-2)-5logx

Mathematics
1 answer:
storchak [24]3 years ago
3 0
Simplify each term<span>.</span>
Simplify <span>3log(x)</span><span> by moving </span>3<span> inside the </span>logarithm<span>. 
</span><span>log(<span>x^3</span>)+2log(y−1)−5log(x)</span><span> 
</span>
Simplify <span>2log(y−1)</span><span> by moving </span>2<span> inside the </span>logarithm<span>. 
</span><span>log(<span>x^3</span>)+log((y−1<span>)^2</span>)−5log(x)</span><span> 
</span>
Rewrite <span>(y−1<span>)^2</span></span><span> as </span><span><span>(y−1)(y−1)</span>.</span><span> 
</span><span>log(<span>x^3</span>)+log((y−1)(y−1))−5log(x)</span><span> 
</span>
Expand <span>(y−1)(y−1)</span><span> using the </span>FOIL<span> Method. 
</span><span>log(<span>x^3</span>)+log(y(y)+y(−1)−1(y)−1(−1))−5log(x)</span><span> 
</span>
Simplify each term<span>. 
</span><span>log(<span>x^3</span>)+log(<span>y^2</span>−2y+1)+log(<span>x^<span>−5</span></span>)</span><span> 

</span>Remove the negative exponent<span> by rewriting </span><span>x^<span>−5</span></span><span> as </span><span><span>1/<span>x^5</span></span>.</span><span> 
</span><span>log(<span>x^3</span>)+log(<span>y^2</span>−2y+1)+log(<span>1/<span>x^5</span></span>)</span><span> 
</span>
Combine<span> logs to get </span><span>log(<span>x^3</span>(<span>y^2</span>−2y+1))
</span><span>log(<span>x^3</span>(<span>y^2</span>−2y+1))+log(<span>1/<span>x^5</span></span>)

</span>Combine<span> logs to get </span><span>log(<span><span><span>x^3</span>(<span>y^2</span>−2y+1)/</span><span>x^5</span></span>)</span><span> 
</span>log(x^3(y^2−2y+1)/x^5)

Cancel <span>x^3</span><span> in the </span>numerator<span> and </span>denominator<span>. 
</span><span>log(<span><span><span>y^2</span>−2y+1/</span><span>x^2</span></span>)</span><span> 

</span>Rewrite 1<span> as </span><span><span>1^2</span>.</span> 
<span><span>y^2</span>−2y+<span>1^2/</span></span><span>x^2</span>

Factor<span> by </span>perfect square<span> rule. 
</span><span>(y−1<span>)^2/</span></span><span>x^2</span>

Replace into larger expression<span>. 
</span>
<span>log(<span><span>(y−1<span>)^2/</span></span><span>x^2</span></span>)</span> 
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August hosted two dinner parties for his friends. Twenty guests attended the first party, and twenty-six guests attended the sec
Ierofanga [76]

Answer: 30%


Step-by-step explanation:

The first step is to find the increase in numbers

26-20= 6

Now you find the percent. This means you're looking for the percent 6 is equal to when compared to 20. The easiest way is to divide the increase by the original number

6/20= 0.3

To convert that to percent, multiply it by 100

0.3 * 100= 30%

There was a 30% increase.

5 0
3 years ago
A rectangular table is fivetimes as long as it is wide. if the area is 80ftsquared​,find the length and the width of the table.
SOVA2 [1]
A = L * W
A = 80
L = 5W

80 = W(5W)
80 = 5W^2
80/5 = W^2
16 = W^2
sqrt 16 = W
4 = W <=== width is 4 ft

L = 5W
L = 5(4)
L = 20 <=== length is 20 ft
3 0
2 years ago
On the blueprint of a house, 42 millimeters represents 8 meters. The actual length of the living room is 5 meters. What is its l
RideAnS [48]

Answer:

26.25 mm

Step-by-step explanation:

On the blueprint of a house, 42 millimeters represents 8 meters. Thus,

42 mm - 8 m,

x mm - 5 m,

mathematically,

\dfrac{42}{x}=\dfrac{8}{5},\\ \\42\cdot 5=8x,\\ \\x=\dfrac{210}{8}=\dfrac{105}{4}=26.25\ mm.

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3 years ago
Inqualities question pls help!
Margaret [11]

Answer:

B

Step-by-step explanation:

The closed circle at - \frac{3}{2} indicates that x can equal this value

The open circle at \frac{7}{2} indicates that x cannot equal this value.

All values of x between - \frac{3}{2} and \frac{7}{2} are valid, thus

- \frac{3}{2} ≤ x < \frac{7}{2} → B

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2 years ago
Use the net to find the lateral area of the cylinder 9yd 4yd
NNADVOKAT [17]

The formula of a lateral area of a cylinder:

LA=2\pi rH

We have r = 9 yd and H = 4 yd. Substitute:

LA=2\pi(9)(4)=72\pi\ yd^2

6 0
3 years ago
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