3 years ago

Choose the correct answer. > < = We can't compare them= fastbridge quiz amath

Mathematics

2 answers:

Feliz [49]3 years ago

8 0

What is the question probably try snapping a picture of what your looking at so I could help

Verizon [17]3 years ago

6 0

Answer:

$\leq$ or $\geq$

Step-by-step explanation:

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2 years ago

Read 2 more answers

<img src="https://tex.z-dn.net/?f=%20log_%7B2%7D%283x%20%2B%204%29%20%20-%207%20log_%7B4%7D%7Bx%7D%5E%7B2%7D%20%20%2B%20%20log_%

olga2289 [7]

First of all, we need all logarithms to have the same base. So, we use the formula

$\log_a(b)=\dfrac{\log_c(b)}{\log_c(a)}$

To change the second term as follows:

$\log_4(x^2)=\dfrac{\log_2(x^2)}{\log_2(4)}=\dfrac{\log_2(x^2)}{2}$

Finally, using the property

$\log(a^b)=b\log(a)$

we have

$\dfrac{\log_2(x^2)}{2}=\log_2(x)$

So, the equation becomes

$\log_2(3x+4)-7\log_2(x)+\log_2(x)=2 \iff \log_2(3x+4)-6\log_2(x)=2$

We can now use the formula

$\log(a)-\log(b)=\log\left(\dfrac{a}{b}\right)$

to write the equation as

$\log_2(3x+4)-6\log_2(x)=2 \iff \log_2(3x+4)-\log_2(x^6)=2 \iff \log_2\left(\dfrac{3x+4}{x^6}\right)=2$

Now consider both sides as exponents of 2:

$\dfrac{3x+4}{x^6}=4 \iff 4x^6-3x-4=0$

This equation has no "nice" solution, so I guess the problem is as simplifies as it can be

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3 years ago