Solve 102*(102^x-1)=11*002

$$102 \times ( { 102 }^{ x } -1)=11 \times 002$$

Solve for x

$$x=0$$

Steps Using Definition of Logarithm

Use the distributive property to multiply 102 by 102^{x}-1.

$$102\times 102^{x}-102=11\times 0\times 0\times 2$$

Multiply 11 and 0 to get 0.

$$102\times 102^{x}-102=0\times 0\times 2$$

Multiply 0 and 0 to get 0.

$$102\times 102^{x}-102=0\times 2$$

Multiply 0 and 2 to get 0.

$$102\times 102^{x}-102=0$$

Add 102 to both sides of the equation.

$$102\times 102^{x}=102$$

Divide both sides by 102.

$$102^{x}=1$$

Take the logarithm of both sides of the equation.

$$\log(102^{x})=\log(1)$$

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

$$x\log(102)=\log(1)$$

Divide both sides by \log(102).

$$x=\frac{\log(1)}{\log(102)}$$

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

$$x=\log_{102}\left(1\right)$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(102)}$$

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