Solve 250000*106^x=297754

$$250000 \times { 106 }^{ x } = 297754$$

Solve for x

$$x=3\log_{106}\left(\frac{53}{50}\right)\approx 0.037484509$$

Steps Using Definition of Logarithm

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

$$250000\times 106^{x}=297754$$

Divide both sides by 250000.

$$106^{x}=\frac{148877}{125000}$$

Take the logarithm of both sides of the equation.

$$\log(106^{x})=\log(\frac{148877}{125000})$$

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

$$x\log(106)=\log(\frac{148877}{125000})$$

Divide both sides by \log(106).

$$x=\frac{\log(\frac{148877}{125000})}{\log(106)}$$

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

$$x=\log_{106}\left(\frac{148877}{125000}\right)$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(106)}+\log_{106}\left(\frac{148877}{125000}\right)$$

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