Solve 2^7x-7=4

$$2 ^ { 7 x - 7 } = 4$$

Solve for x

$$x = \frac{9}{7} = 1\frac{2}{7} \approx 1.285714286$$

Steps Using Definition of Logarithm

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

$$2^{7x-7}=4$$

Take the logarithm of both sides of the equation.

$$\log(2^{7x-7})=\log(4)$$

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

$$\left(7x-7\right)\log(2)=\log(4)$$

Divide both sides by \log(2).

$$7x-7=\frac{\log(4)}{\log(2)}$$

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

$$7x-7=\log_{2}\left(4\right)$$

Add 7 to both sides of the equation.

$$7x=2-\left(-7\right)$$

Divide both sides by 7.

$$x=\frac{9}{7}$$

Solve for x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{7\ln(2)}+\frac{9}{7}$$

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