Solve 6^2n+1div36=6^3

$$6 ^ { 2 n + 1 } \div 36 = 6 ^ { 3 }$$

Solve for n

$$n=2$$

Steps Using Definition of Logarithm

Use the rules of exponents and logarithms to solve the equation.

$$\frac{1}{36}\times 6^{2n+1}=216$$

Multiply both sides by 36.

$$6^{2n+1}=7776$$

Take the logarithm of both sides of the equation.

$$\log(6^{2n+1})=\log(7776)$$

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

$$\left(2n+1\right)\log(6)=\log(7776)$$

Divide both sides by \log(6).

$$2n+1=\frac{\log(7776)}{\log(6)}$$

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

$$2n+1=\log_{6}\left(7776\right)$$

Subtract 1 from both sides of the equation.

$$2n=5-1$$

Divide both sides by 2.

$$n=\frac{4}{2}$$