Solve 6x^n-4m+7=2

$$6 x ^ { n } - 4 m + 7 = 2$$

Solve for m (complex solution)

$$m=\frac{3x^{n}}{2}+\frac{5}{4}$$

Steps for Solving Linear Equation

Subtract 6x^{n} from both sides.

$$-4m+7=2-6x^{n}$$

Subtract 7 from both sides.

$$-4m=2-6x^{n}-7$$

Subtract 7 from 2 to get -5.

$$-4m=-5-6x^{n}$$

The equation is in standard form.

$$-4m=-6x^{n}-5$$

Divide both sides by -4.

$$\frac{-4m}{-4}=\frac{-6x^{n}-5}{-4}$$

Dividing by -4 undoes the multiplication by -4.

$$m=\frac{-6x^{n}-5}{-4}$$

Divide -5-6x^{n} by -4.

$$m=\frac{3x^{n}}{2}+\frac{5}{4}$$

Solve for m

$$m=\frac{3x^{n}}{2}+\frac{5}{4}$$

$$\left(x<0\text{ and }Denominator(n)\text{bmod}2=1\right)\text{ or }\left(x=0\text{ and }n>0\right)\text{ or }x>0$$

Steps for Solving Linear Equation

Subtract 6x^{n} from both sides.

$$-4m+7=2-6x^{n}$$

Subtract 7 from both sides.

$$-4m=2-6x^{n}-7$$

Subtract 7 from 2 to get -5.

$$-4m=-5-6x^{n}$$

The equation is in standard form.

$$-4m=-6x^{n}-5$$

Divide both sides by -4.

$$\frac{-4m}{-4}=\frac{-6x^{n}-5}{-4}$$

Dividing by -4 undoes the multiplication by -4.

$$m=\frac{-6x^{n}-5}{-4}$$

Divide -5-6x^{n} by -4.

$$m=\frac{3x^{n}}{2}+\frac{5}{4}$$

Solve for n (complex solution)

$$\left\{\begin{matrix}n=\frac{2\pi n_{1}i}{\ln(x)}+\log_{x}\left(\frac{2m}{3}-\frac{5}{6}\right)\text{, }n_{1}\in \mathrm{Z}\text{, }&m\neq \frac{5}{4}\text{ and }x\neq 1\text{ and }x\neq 0\\n\in \mathrm{C}\text{, }&\left(x=0\text{ and }m=\frac{5}{4}\right)\text{ or }\left(x=1\text{ and }m=\frac{11}{4}\right)\end{matrix}\right.$$

Solve for n

$$\left\{\begin{matrix}n=\log_{x}\left(\frac{2m}{3}-\frac{5}{6}\right)\text{, }&m>\frac{5}{4}\text{ and }x\neq 1\text{ and }x>0\\n\in \mathrm{R}\text{, }&\left(x=1\text{ and }m=\frac{11}{4}\right)\text{ or }\left(x=-1\text{ and }m=-\frac{1}{4}\text{ and }Denominator(n)\text{bmod}2=1\text{ and }Numerator(n)\text{bmod}2=1\right)\\n>0\text{, }&x=0\text{ and }m=\frac{5}{4}\end{matrix}\right.$$