Solve 27^2x=98

$$27 ^ { 2 x } = 98$$

Solve for x

$$x=\frac{\log_{3}\left(98\right)}{6}\approx 0.695569542$$

Steps Using Definition of Logarithm

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

$$27^{2x}=98$$

Take the logarithm of both sides of the equation.

$$\log(27^{2x})=\log(98)$$

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

$$2x\log(27)=\log(98)$$

Divide both sides by \log(27).

$$2x=\frac{\log(98)}{\log(27)}$$

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

$$2x=\log_{27}\left(98\right)$$

Divide both sides by 2.

$$x=\frac{\log_{3}\left(98\right)}{2\times 3}$$

Solve for x (complex solution)

$$x=\frac{\pi n_{1}i}{3\ln(3)}+\frac{\log_{3}\left(98\right)}{6}$$

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