Solve 2^1,5x-3=64

$$2 ^ { 1,5 x - 3 } = 64$$

Solve for x

$$x=6$$

Steps Using Definition of Logarithm

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

$$2^{1,5x-3}=64$$

Take the logarithm of both sides of the equation.

$$\log(2^{1,5x-3})=\log(64)$$

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

$$\left(1,5x-3\right)\log(2)=\log(64)$$

Divide both sides by \log(2).

$$1,5x-3=\frac{\log(64)}{\log(2)}$$

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

$$1,5x-3=\log_{2}\left(64\right)$$

Add 3 to both sides of the equation.

$$1,5x=6-\left(-3\right)$$

Divide both sides of the equation by 1,5, which is the same as multiplying both sides by the reciprocal of the fraction.

$$x=\frac{9}{1,5}$$