Solve 2^31*4^50div2=4^5x

$${ 2 }^{ 31 } \times { 4 }^{ 50 } \div 2= { 4 }^{ 5x }$$

Solve for x

$$x=13$$

Steps Using Definition of Logarithm

Multiply both sides of the equation by 2.

$$2^{31}\times 4^{50}=2\times 4^{5x}$$

Calculate 2 to the power of 31 and get 2147483648.

$$2147483648\times 4^{50}=2\times 4^{5x}$$

Calculate 4 to the power of 50 and get 1267650600228229401496703205376.

$$2147483648\times 1267650600228229401496703205376=2\times 4^{5x}$$

Multiply 2147483648 and 1267650600228229401496703205376 to get 2722258935367507707706996859454145691648.

$$2722258935367507707706996859454145691648=2\times 4^{5x}$$

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

$$2\times 4^{5x}=2722258935367507707706996859454145691648$$

Divide both sides by 2.

$$4^{5x}=\frac{2722258935367507707706996859454145691648}{2}$$

Divide 2722258935367507707706996859454145691648 by 2 to get 1361129467683753853853498429727072845824.

$$4^{5x}=1361129467683753853853498429727072845824$$

Take the logarithm of both sides of the equation.

$$\log(4^{5x})=\log(1361129467683753853853498429727072845824)$$

The logarithm of a number raised to a power is the power times the logarithm of the number.

$$5x\log(4)=\log(1361129467683753853853498429727072845824)$$

Divide both sides by \log(4).

$$5x=\frac{\log(1361129467683753853853498429727072845824)}{\log(4)}$$

By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).

$$5x=\log_{4}\left(1361129467683753853853498429727072845824\right)$$

Divide both sides by 5.

$$x=\frac{65}{5}$$

Solve for x (complex solution)

$$x=\frac{i\pi n_{1}}{5\ln(2)}+13$$

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