Mixed Equations

We can classify an equation of the form

as

• linear ($blabla$ consists of $x$-terms and number terms)
• quadratic ($blabla$ consists of $x^2$ terms, $x$ terms and a number term)
• exponential ($blabla$ consists of exponential terms $number^x$ and number terms)
• logarithmic ($blabla$ consists of $\log$ terms and number terms)
• equations with powers ($blabla$ consists of $x^{number}$ terms and number terms)
• a system of linear equations
• something else

Below are given some equations. Classify them, and then solve them using the calculator. Check the result by substituting.

A) First the basic forms

1. $3x+2 = 0$
2. $x^2-5x+6 = 0$
3. $-2x^2+4x-7=0$
4. $x^5-12=0$
5. $x^{-2}-2 =0$
6. $x^{2/3}-2 = 0$
7. $\log_7(x)-2=0$
8. $7^x -2 =0$
9. $x^{-0.7} -4=0$
10. $3x^2-4x = 0$
11. $\log_5(x)+\frac{1}{2}=0$
12. $11^{x} -5 =0$
13. $4^x-9=0$
14. $x^{-4}-2=0$
15. $x^7+9=0$
16. $x^2-x-1 =0$
17. $\left\vert\begin{array}{lll} 3x-4y-1 & = & 0\\ x+5y+8 & = & 0\end{array}\right\vert$
18. $\left\vert\begin{array}{lll} 10x+5y-1 & = & 0\\ 10x-3y+8 & = & 0\end{array}\right\vert$

B) A bit more variations, with coefficients

1. $4x+4-7x-6+9=x-1$
2. $4x^2-2x+1-2x^2-x=x^2-1$
3. $2\log_3(x)-5 =0$
4. $2x^2=5x$
5. $3\cdot 2^{x}-10=0$
6. $3x^{1/3}-4=0$
7. $\frac{1}{2} x^{1/2} -2=0$
8. $-2e^x +4=0$
9. $4 x^{-2/3} -16 = 0$
10. $10\log_2(x)+3=0$
11. $0.2 x^{-0.75} -1.5 = 0$

C) Here the power rules might help

1. $(x-1)(x+3)=0$
2. $6\log_3(x^2-1)+1=0$
3. $1.5 e^{4x-1} -2.5 = 0$
4. $\frac{1}{x^2} -10 = 0$
5. $2\sqrt{x}-1=0$
6. $x(x-2)=0$
7. $3\sqrt[5]{x^2} -3 =0$
8. $\frac{7}{\sqrt{x^3}} -3 = 0$
9. $3e^{\frac{x-2}{5}}-4=0$
10. $x^2(2-3x)=0$
11. $\frac{3}{4x^2}-2=1$
12. $\left\vert\begin{array}{lll} \frac{1}{4}x-2y+\frac{3}{5} & = & 0\\ -\frac{1}{3}x+\frac{3}{8}y-\frac{1}{2} & = & 0\end{array}\right\vert$
13. $\sqrt[3]{x^2-4}-2=0$
14. $\frac{2}{x+1}+1=0$