Solve 6^4x-9=36^1,5

$$6 ^ { 4 x - 9 } = 36 ^ { 1,5 }$$

Solve for x

$$x=3$$

Steps Using Definition of Logarithm

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

$$6^{4x-9}=216$$

Take the logarithm of both sides of the equation.

$$\log(6^{4x-9})=\log(216)$$

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

$$\left(4x-9\right)\log(6)=\log(216)$$

Divide both sides by \log(6).

$$4x-9=\frac{\log(216)}{\log(6)}$$

By the change-of-base formula log(a)/log(b)=log(b,a).

$$4x-9=\log_{6}\left(216\right)$$

Add 9 to both sides of the equation.

$$4x=3-\left(-9\right)$$

Divide both sides by 4.

$$x=\frac{12}{4}$$