Solve 2.7^2x=98

$$2.7 ^ { 2 x } = 98$$

Solve for x

$$x = \frac{\log_{2.7} {(98)}}{2} \approx 2.308059046$$

Steps Using Definition of Logarithm

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

$$2.7^{2x}=98$$

Take the logarithm of both sides of the equation.

$$\log(2.7^{2x})=\log(98)$$

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

$$2x\log(2.7)=\log(98)$$

Divide both sides by \log(2.7).

$$2x=\frac{\log(98)}{\log(2.7)}$$

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

$$2x=\log_{2.7}\left(98\right)$$

Divide both sides by 2.

$$x=\frac{\ln(98)}{2\ln(\frac{27}{10})}$$

Solve for x (complex solution)

$$x=\frac{i\pi n_{1}}{\ln(2.7)}+\frac{\log_{2.7}\left(98\right)}{2}$$

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