Solve (1/2)^-5X(1/3)^-10=(1/3)^3x

$$( \frac { 1 } { 2 } ) ^ { - 5 } X ( \frac { 1 } { 3 } ) ^ { - 10 } = ( \frac { 1 } { 3 } ) ^ { 3 x }$$

Solve for X

$$X=\frac{\left(\frac{1}{27}\right)^{x}}{1889568}$$

Steps for Solving Linear Equation

Calculate \frac{1}{2} to the power of -5 and get 32.

$$32X\times \left(\frac{1}{3}\right)^{-10}=\left(\frac{1}{3}\right)^{3x}$$

Calculate \frac{1}{3} to the power of -10 and get 59049.

$$32X\times 59049=\left(\frac{1}{3}\right)^{3x}$$

Multiply 32 and 59049 to get 1889568.

$$1889568X=\left(\frac{1}{3}\right)^{3x}$$

The equation is in standard form.

$$1889568X=\left(\frac{1}{27}\right)^{x}$$

Divide both sides by 1889568.

$$\frac{1889568X}{1889568}=\frac{\left(\frac{1}{27}\right)^{x}}{1889568}$$

Dividing by 1889568 undoes the multiplication by 1889568.

$$X=\frac{\left(\frac{1}{27}\right)^{x}}{1889568}$$

Solve for x (complex solution)

$$x=\frac{-\ln(X)+\ln(\frac{1}{1889568})}{3\ln(3)}-\frac{2\pi n_{1}i}{3\ln(3)}$$

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

$$X\neq 0$$

Solve for x

$$x=\frac{-\ln(X)+\ln(\frac{1}{1889568})}{3\ln(3)}$$

$$X>0$$