Solve 4802=2*7^x-1

$$4802=2 \times { 7 }^{ x-1 }$$

Solve for x

$$x=5$$

Steps Using Definition of Logarithm

Divide both sides by 2.

$$\frac{4802}{2}=7^{x-1}$$

Divide 4802 by 2 to get 2401.

$$2401=7^{x-1}$$

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

$$7^{x-1}=2401$$

Take the logarithm of both sides of the equation.

$$\log(7^{x-1})=\log(2401)$$

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

$$\left(x-1\right)\log(7)=\log(2401)$$

Divide both sides by \log(7).

$$x-1=\frac{\log(2401)}{\log(7)}$$

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

$$x-1=\log_{7}\left(2401\right)$$

Add 1 to both sides of the equation.

$$x=4-\left(-1\right)$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(7)}+5$$

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