Solve 15^t^2/10x^2=20/n

$$\frac { 15 ^ { t ^ { 2 } } } { 10 x ^ { 2 } } = \frac { 20 } { n }$$

Solve for n

$$n=\frac{200x^{2}}{15^{t^{2}}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Variable n cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 10nx^{2}, the least common multiple of 10x^{2},n.

$$n\times 15^{t^{2}}=10x^{2}\times 20$$

Multiply 10 and 20 to get 200.

$$n\times 15^{t^{2}}=200x^{2}$$

The equation is in standard form.

$$15^{t^{2}}n=200x^{2}$$

Divide both sides by 15^{t^{2}}.

$$\frac{15^{t^{2}}n}{15^{t^{2}}}=\frac{200x^{2}}{15^{t^{2}}}$$

Dividing by 15^{t^{2}} undoes the multiplication by 15^{t^{2}}.

$$n=\frac{200x^{2}}{15^{t^{2}}}$$

Variable n cannot be equal to 0.

$$n=\frac{200x^{2}}{15^{t^{2}}}\text{, }n\neq 0$$

Solve for t

$$t=\sqrt{\frac{\ln(\frac{x^{2}}{n})+\ln(200)}{\ln(15)}}$$

$$t=-\sqrt{\frac{\ln(\frac{x^{2}}{n})+\ln(200)}{\ln(15)}}\text{, }x\neq 0\text{ and }n>0\text{ and }|x|\geq \frac{\sqrt{2n}}{20}$$