Answer:
wat is the quistion
Step-by-step explanation:
The value of x is -1.596
<em><u>Solution:</u></em>
<em><u>Given equation is:</u></em>
![4^{(x+3)} = 7](https://tex.z-dn.net/?f=4%5E%7B%28x%2B3%29%7D%20%3D%207)
Let us solve using change of base formula log base b of y equals log y over log b
From given,
![4^{(x+3)} = 7](https://tex.z-dn.net/?f=4%5E%7B%28x%2B3%29%7D%20%3D%207)
![\mathrm{If\:}f\left(x\right)=g\left(x\right)\mathrm{,\:then\:}\ln \left(f\left(x\right)\right)=\ln \left(g\left(x\right)\right)](https://tex.z-dn.net/?f=%5Cmathrm%7BIf%5C%3A%7Df%5Cleft%28x%5Cright%29%3Dg%5Cleft%28x%5Cright%29%5Cmathrm%7B%2C%5C%3Athen%5C%3A%7D%5Cln%20%5Cleft%28f%5Cleft%28x%5Cright%29%5Cright%29%3D%5Cln%20%5Cleft%28g%5Cleft%28x%5Cright%29%5Cright%29)
Therefore,
![\ln \left(4^{x+3}\right)=\ln \left(7\right)](https://tex.z-dn.net/?f=%5Cln%20%5Cleft%284%5E%7Bx%2B3%7D%5Cright%29%3D%5Cln%20%5Cleft%287%5Cright%29)
![\mathrm{Apply\:log\:rule}:\quad \log _a\left(x^b\right)=b\cdot \log _a\left(x\right)](https://tex.z-dn.net/?f=%5Cmathrm%7BApply%5C%3Alog%5C%3Arule%7D%3A%5Cquad%20%5Clog%20_a%5Cleft%28x%5Eb%5Cright%29%3Db%5Ccdot%20%5Clog%20_a%5Cleft%28x%5Cright%29)
![\ln \left(4^{x+3}\right)=\left(x+3\right)\ln \left(4\right)\\\\\left(x+3\right)\ln \left(4\right)=\ln \left(7\right)\\](https://tex.z-dn.net/?f=%5Cln%20%5Cleft%284%5E%7Bx%2B3%7D%5Cright%29%3D%5Cleft%28x%2B3%5Cright%29%5Cln%20%5Cleft%284%5Cright%29%5C%5C%5C%5C%5Cleft%28x%2B3%5Cright%29%5Cln%20%5Cleft%284%5Cright%29%3D%5Cln%20%5Cleft%287%5Cright%29%5C%5C)
Let us simplify the above
![\left(x+3\right)\cdot \:2\ln \left(2\right)=\ln \left(7\right)\\\\\mathrm{Divide\:both\:sides\:by\:}2\ln \left(2\right)\\\\\frac{\left(x+3\right)\cdot \:2\ln \left(2\right)}{2\ln \left(2\right)}=\frac{\ln \left(7\right)}{2\ln \left(2\right)}\\\\](https://tex.z-dn.net/?f=%5Cleft%28x%2B3%5Cright%29%5Ccdot%20%5C%3A2%5Cln%20%5Cleft%282%5Cright%29%3D%5Cln%20%5Cleft%287%5Cright%29%5C%5C%5C%5C%5Cmathrm%7BDivide%5C%3Aboth%5C%3Asides%5C%3Aby%5C%3A%7D2%5Cln%20%5Cleft%282%5Cright%29%5C%5C%5C%5C%5Cfrac%7B%5Cleft%28x%2B3%5Cright%29%5Ccdot%20%5C%3A2%5Cln%20%5Cleft%282%5Cright%29%7D%7B2%5Cln%20%5Cleft%282%5Cright%29%7D%3D%5Cfrac%7B%5Cln%20%5Cleft%287%5Cright%29%7D%7B2%5Cln%20%5Cleft%282%5Cright%29%7D%5C%5C%5C%5C)
![\mathrm{Simplify}\\\\x+3=\frac{\ln \left(7\right)}{2\ln \left(2\right)}\\\\\mathrm{Subtract\:}3\mathrm{\:from\:both\:sides}\\\\x+3-3=\frac{\ln \left(7\right)}{2\ln \left(2\right)}-3\\\\\mathrm{Simplify}\\\\x=\frac{\ln \left(7\right)}{2\ln \left(2\right)}-3](https://tex.z-dn.net/?f=%5Cmathrm%7BSimplify%7D%5C%5C%5C%5Cx%2B3%3D%5Cfrac%7B%5Cln%20%5Cleft%287%5Cright%29%7D%7B2%5Cln%20%5Cleft%282%5Cright%29%7D%5C%5C%5C%5C%5Cmathrm%7BSubtract%5C%3A%7D3%5Cmathrm%7B%5C%3Afrom%5C%3Aboth%5C%3Asides%7D%5C%5C%5C%5Cx%2B3-3%3D%5Cfrac%7B%5Cln%20%5Cleft%287%5Cright%29%7D%7B2%5Cln%20%5Cleft%282%5Cright%29%7D-3%5C%5C%5C%5C%5Cmathrm%7BSimplify%7D%5C%5C%5C%5Cx%3D%5Cfrac%7B%5Cln%20%5Cleft%287%5Cright%29%7D%7B2%5Cln%20%5Cleft%282%5Cright%29%7D-3)
Substitute the values
ln 7 = 1.9459101490553132
ln 2 = 0.6931471805599453
Therefore,
![x = \frac{1.9459101490553132}{2 \times 0.6931471805599453} - 3\\\\x = 1.40367746103 - 3\\\\x = -1.59632253897 \approx -1.596](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B1.9459101490553132%7D%7B2%20%5Ctimes%200.6931471805599453%7D%20-%203%5C%5C%5C%5Cx%20%3D%201.40367746103%20-%203%5C%5C%5C%5Cx%20%3D%20-1.59632253897%20%5Capprox%20-1.596)
Thus solution for x is found
Answer:
Correct option: first one -> all real values of x where x < −1
Step-by-step explanation:
First we need to find the roots of the function f(x):
0 = (x - 3)(x + 1)
(x - 3) = 0 -> x = 3
(x + 1) = 0 -> x = -1
The roots of the function are x = 3 and x = -1.
The vertex is between the roots (x = 1) and has a negative value of y (y = -4), so the concavity of the parabola is upwards.
So the graph is decreasing until it reaches the vertex, then the graph is increasing.
Then, we can affirm that the graph is positive and decreasing for all real values of x where x < -1 (for x > -1 and x < 3 we have negative values)
Correct option: first one
Answer:
18
Step-by-step explanation:
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