Solve B(1/27)^x=1/9

$$B ( \frac { 1 } { 27 } ) ^ { x } = \frac { 1 } { 9 }$$

Solve for B

$$B=\frac{27^{x}}{9}$$

Steps for Solving Linear Equation

The equation is in standard form.

$$\left(\frac{1}{27}\right)^{x}B=\frac{1}{9}$$

Divide both sides by \left(\frac{1}{27}\right)^{x}.

$$\frac{\left(\frac{1}{27}\right)^{x}B}{\left(\frac{1}{27}\right)^{x}}=\frac{\frac{1}{9}}{\left(\frac{1}{27}\right)^{x}}$$

Dividing by \left(\frac{1}{27}\right)^{x} undoes the multiplication by \left(\frac{1}{27}\right)^{x}.

$$B=\frac{\frac{1}{9}}{\left(\frac{1}{27}\right)^{x}}$$

Divide \frac{1}{9} by \left(\frac{1}{27}\right)^{x}.

$$B=\frac{27^{x}}{9}$$

Solve for x (complex solution)

$$x=\frac{\log_{3}\left(B\right)}{3}-\frac{2\pi n_{1}i}{3\ln(3)}+\frac{2}{3}$$

$$n_{1}\in \mathrm{Z}$$

$$B\neq 0$$

Solve for x

$$x=\frac{\log_{3}\left(B\right)+2}{3}$$

$$B>0$$