Solve 3^2x*3^6=5^frac{1{2}}ydiv5

$$3 ^ { 2 x } \times 3 ^ { 6 } = 5 ^ { \frac { 1 } { 2 } } y \div 5$$

Solve for y

$$y=729\sqrt{5}\times 9^{x}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 5.

$$5\times 3^{2x}\times 3^{6}=5^{\frac{1}{2}}y$$

Calculate 3 to the power of 6 and get 729.

$$5\times 3^{2x}\times 729=5^{\frac{1}{2}}y$$

Multiply 5 and 729 to get 3645.

$$3645\times 3^{2x}=5^{\frac{1}{2}}y$$

Swap sides so that all variable terms are on the left hand side.

$$5^{\frac{1}{2}}y=3645\times 3^{2x}$$

Reorder the terms.

$$\sqrt{5}y=3645\times 3^{2x}$$

The equation is in standard form.

$$\sqrt{5}y=3645\times 9^{x}$$

Divide both sides by \sqrt{5}.

$$\frac{\sqrt{5}y}{\sqrt{5}}=\frac{3645\times 9^{x}}{\sqrt{5}}$$

Dividing by \sqrt{5} undoes the multiplication by \sqrt{5}.

$$y=\frac{3645\times 9^{x}}{\sqrt{5}}$$

Divide 3645\times 9^{x} by \sqrt{5}.

$$y=729\sqrt{5}\times 9^{x}$$

Solve for x (complex solution)

$$x=\frac{2\ln(y)+\ln(\frac{1}{2657205})}{4\ln(3)}+\frac{\pi n_{1}i}{\ln(3)}$$

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

$$y\neq 0$$

Solve for x

$$x=\frac{2\ln(y)+\ln(\frac{1}{2657205})}{4\ln(3)}$$

$$y>0$$