Solve {left(25/36right)}^342^3*24^4/140^2=10^x*{y}^1

$${ \left( \frac{ 25 }{ 36 } \right) }^{ 3 } \frac{ { 42 }^{ 3 } \times { 24 }^{ 4 } }{ { 140 }^{ 2 } } = { 10 }^{ x } \times { y }^{ 1 }$$

Solve for y

$$y=\frac{420000}{10^{x}}$$

Steps for Solving Linear Equation

Calculate \frac{25}{36} to the power of 3 and get \frac{15625}{46656}.

$$\frac{15625}{46656}\times \frac{42^{3}\times 24^{4}}{140^{2}}=10^{x}y^{1}$$

Calculate 42 to the power of 3 and get 74088.

$$\frac{15625}{46656}\times \frac{74088\times 24^{4}}{140^{2}}=10^{x}y^{1}$$

Calculate 24 to the power of 4 and get 331776.

$$\frac{15625}{46656}\times \frac{74088\times 331776}{140^{2}}=10^{x}y^{1}$$

Multiply 74088 and 331776 to get 24580620288.

$$\frac{15625}{46656}\times \frac{24580620288}{140^{2}}=10^{x}y^{1}$$

Calculate 140 to the power of 2 and get 19600.

$$\frac{15625}{46656}\times \frac{24580620288}{19600}=10^{x}y^{1}$$

Reduce the fraction \frac{24580620288}{19600} to lowest terms by extracting and canceling out 784.

$$\frac{15625}{46656}\times \frac{31352832}{25}=10^{x}y^{1}$$

Multiply \frac{15625}{46656} and \frac{31352832}{25} to get 420000.

$$420000=10^{x}y^{1}$$

Calculate y to the power of 1 and get y.

$$420000=10^{x}y$$

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

$$10^{x}y=420000$$

Divide both sides by 10^{x}.

$$\frac{10^{x}y}{10^{x}}=\frac{420000}{10^{x}}$$

Dividing by 10^{x} undoes the multiplication by 10^{x}.

$$y=\frac{420000}{10^{x}}$$

Solve for x (complex solution)

$$x=\log(e)\left(-\ln(y)+\ln(420000)\right)+2\pi n_{1}i\log(e)$$

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

$$y\neq 0$$

Solve for x

$$x=\log(e)\left(-\ln(y)+\ln(420000)\right)$$

$$y>0$$