Solve 12.2=2(10^1.2x)-9.2

$$12.2 = 2 ( 10 ^ { 1.2 x } ) - 9.2$$

Solve for x

$$x=\frac{5\log(107)-5}{6}\approx 0.857819815$$

Steps Using Definition of Logarithm

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

$$2\times 10^{1.2x}-9.2=12.2$$

Add 9.2 to both sides of the equation.

$$2\times 10^{1.2x}=21.4$$

Divide both sides by 2.

$$10^{1.2x}=10.7$$

Take the logarithm of both sides of the equation.

$$\log(10^{1.2x})=\log(10.7)$$

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

$$1.2x\log(10)=\log(10.7)$$

Divide both sides of the equation by 1.2, which is the same as multiplying both sides by the reciprocal of the fraction.

$$x=\frac{\log(107)-1}{1.2}$$

Solve for x (complex solution)

$$x=\frac{i\times 5\pi n_{1}\log(e)}{3}+\frac{5\left(\log(107)-1\right)}{6}$$

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