Solve 47000000div9428=123^x

$$47000000 \div 9428 = { 123 }^{ x }$$

Solve for x

$$x=\log_{123}\left(\frac{11750000}{2357}\right)\approx 1.769304388$$

Steps Using Definition of Logarithm

Reduce the fraction \frac{47000000}{9428} to lowest terms by extracting and canceling out 4.

$$\frac{11750000}{2357}=123^{x}$$

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

$$123^{x}=\frac{11750000}{2357}$$

Take the logarithm of both sides of the equation.

$$\log(123^{x})=\log(\frac{11750000}{2357})$$

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

$$x\log(123)=\log(\frac{11750000}{2357})$$

Divide both sides by \log(123).

$$x=\frac{\log(\frac{11750000}{2357})}{\log(123)}$$

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

$$x=\log_{123}\left(\frac{11750000}{2357}\right)$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(123)}+\log_{123}\left(\frac{11750000}{2357}\right)$$

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