Solve 5*9^x-1=5

$$5 \times 9 ^ { x - 1 } = 5$$

Solve for x

$$x=1$$

Steps Using Definition of Logarithm

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

$$5\times 9^{x-1}=5$$

Divide both sides by 5.

$$9^{x-1}=1$$

Take the logarithm of both sides of the equation.

$$\log(9^{x-1})=\log(1)$$

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

$$\left(x-1\right)\log(9)=\log(1)$$

Divide both sides by \log(9).

$$x-1=\frac{\log(1)}{\log(9)}$$

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

$$x-1=\log_{9}\left(1\right)$$

Add 1 to both sides of the equation.

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

Solve for x (complex solution)

$$x=\frac{\pi n_{1}i}{\ln(3)}+1$$

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