Solve 3^x+1=(273/10)^4

$$3 ^ { x + 1 } = ( \frac { 273 } { 10 } ) ^ { 4 }$$

Solve for x

$$x=\log_{3}\left(\frac{68574961}{10000}\right)+3\approx 11.040231977$$

Steps Using Definition of Logarithm

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

$$3^{x+1}=\frac{5554571841}{10000}$$

Take the logarithm of both sides of the equation.

$$\log(3^{x+1})=\log(\frac{5554571841}{10000})$$

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

$$\left(x+1\right)\log(3)=\log(\frac{5554571841}{10000})$$

Divide both sides by \log(3).

$$x+1=\frac{\log(\frac{5554571841}{10000})}{\log(3)}$$

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

$$x+1=\log_{3}\left(\frac{5554571841}{10000}\right)$$

Subtract 1 from both sides of the equation.

$$x=\frac{\ln(\frac{5554571841}{10000})}{\ln(3)}-1$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(3)}+\log_{3}\left(\frac{68574961}{10000}\right)+3$$

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