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Karolina [17]
3 years ago
12

Simplify the expression below and write it as a single logarithm:

Mathematics
2 answers:
BabaBlast [244]3 years ago
5 0

Answer:

log((x+4)^3)x-7)^2 / (x-2)^5 x^2)

Step-by-step explanation:

OLEGan [10]3 years ago
4 0

The simplification of 3log(x + 4) – 2log(x – 7) + 5log(x - 2) - log(x^2) is \log \left(\frac{(x+4)^{3} \times(x-2)^{5}}{(x-7)^{2} \times x^{2}}\right)

<u>Solution:</u>

Given, expression is 3 \log (x+4)-2 \log (x-7)+5 \log (x-2)-\log \left(x^{2}\right)

We have to write in as single logarithm by simplifying it.

Now, take the given expression.

\rightarrow 3 \log (x+4)-2 \log (x-7)+5 \log (x-2)-\log \left(x^{2}\right)

Rearranging the terms we get,

\left.\rightarrow 3 \log (x+4)+5 \log (x-2)-2 \log (x-7)+\log \left(x^{2}\right)\right)

\text { since a } \times \log b=\log \left(b^{a}\right)

\rightarrow \log (x+4)^{3}+\log (x-2)^{5}-\left(\log (x-7)^{2}+\log \left(x^{2}\right)\right)

\text { We know that } \log a \times \log b=\log a b

\rightarrow \log \left((x+4)^{3} \times(x-2)^{5}\right)-\left(\log \left((x-7)^{2} \times\left(x^{2}\right)\right)\right.

\text { We know that } \log a-\log b=\log \frac{a}{b}

\rightarrow \log \left(\frac{(x+4)^{3} \times(x-2)^{5}}{(x-7)^{2} \times x^{2}}\right)

Hence, the simplified form \rightarrow \log \left(\frac{(x+4)^{3} \times(x-2)^{5}}{(x-7)^{2} \times x^{2}}\right)

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olga55 [171]

Answer:

candles = $400

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Step-by-step explanation:

Let cost of candles = $c

Let cost of matches = $m

c = 20 m (20 times m)

c + m = 420

20m + m = 420

21 m = 420

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Step-by-step explanation:

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15. The height and yolume of a cylinder are 4cm and 616cm respectively. Calculate the diameter of the base. (take t = 27 쪽 A. 7c
irakobra [83]

Step-by-step explanation:

Given that,

  • Height of cylinder = 4 cm
  • Volume of cylinder = 616 cm³

To find,

  • Diameter of the base = ?

Firstly we'll find the base radius of the cylinder.

\longmapsto\rm{V_{(Cylinder)} = \pi r^2h}\\

<u>Accordi</u><u>ng</u><u> </u><u>to</u><u> </u><u>the</u><u> </u><u>qu</u><u>estion</u><u>,</u>

\longmapsto\rm{616= \dfrac{22}{7} \times r^2 \times 4}\\

\longmapsto\rm{616 \times 7 = 22 \times r^2 \times 4}\\

\longmapsto\rm{4312 = 88 \times r^2 }\\

\longmapsto\rm{\cancel{\dfrac{4312}{88}} =  r^2 }\\

\longmapsto\rm{49 =  r^2 }\\

\longmapsto\rm{\sqrt{49} =  r }\\

\longmapsto\rm{7 \; cm =  r }\\

Now,

\longmapsto\rm{Diameter = 2r }\\

\longmapsto\rm{Diameter = 2(7 \; cm) }\\

\longmapsto\bf{Diameter = 14 \; cm}\\

The required answer is 14 cm.

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Stells [14]
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3 0
2 years ago
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