138.4divided by16 show works it possible to show your work

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

OLEGan [10]

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

Solution:

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

4 0

3 years ago

Read 2 more answers

Find the slope of a line through the following pair of points:

Zinaida [17]

No slope i believe. good luck!

6 0

3 years ago

Your shop employs seven people. Today two people are sick. What fraction represents the employees who are sick

Feliz [49]

Answer:

2/7 of represents employees who are sick

Step-by-step explanation:

Question:

What fraction represents the employees who are sick

Total People = 7

sick people =2

numerator/denominator

2/7

8 0

2 years ago

Mr. Scruggs got some money for his birthday. He spent 1/5 of it on dog treats. Then, he divided the remainder equally among his

andrew-mc [135]

Let the amount of money be M,

then Mr.Scruggs spent 1/5M on dog treats, and so 4/5M was left.

4/5M was equally divided in 3 parts among his favourite charities, so each of these received:
 $\frac{ \frac{4}{5}M }{3}=\frac{4}{5}M* \frac{1}{3}=\frac{4}{15}M$

i) each charity received 4/15 of the money.

ii)
 $\frac{4}{15}M=$60$

4M=15*60
M=15*15

M= 225 (dollars).

Check: 4/5(225)=4*45=180, 180/3=60

5 0

3 years ago

Which size is better in buying detergent: 32 fl oz for $1.99 50fl oz for $2.49

8_murik_8 [283]

the 32oz is more expensive per oz. by $.01 per oz.

5 0

3 years ago