Solve 144489/800=103^x

$$\frac{ 144489 }{ 800 } = { 103 }^{ x }$$

Solve for x

$$x=\log_{103}\left(\frac{144489}{800}\right)\approx 1.121176005$$

Steps Using Definition of Logarithm

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

$$103^{x}=\frac{144489}{800}$$

Take the logarithm of both sides of the equation.

$$\log(103^{x})=\log(\frac{144489}{800})$$

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

$$x\log(103)=\log(\frac{144489}{800})$$

Divide both sides by \log(103).

$$x=\frac{\log(\frac{144489}{800})}{\log(103)}$$

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

$$x=\log_{103}\left(\frac{144489}{800}\right)$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(103)}+\log_{103}\left(\frac{144489}{800}\right)$$

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