Solve 1.1*1.3^x-14=10.6

$$1.1 \times { 1.3 }^{ x } -14=10.6$$

Solve for x

$$x=\log_{1.3}\left(\frac{246}{11}\right)\approx 11.843976806$$

Steps Using Definition of Logarithm

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

$$1.1\times 1.3^{x}-14=10.6$$

Add 14 to both sides of the equation.

$$1.1\times 1.3^{x}=24.6$$

Divide both sides of the equation by 1.1, which is the same as multiplying both sides by the reciprocal of the fraction.

$$1.3^{x}=\frac{246}{11}$$

Take the logarithm of both sides of the equation.

$$\log(1.3^{x})=\log(\frac{246}{11})$$

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

$$x\log(1.3)=\log(\frac{246}{11})$$

Divide both sides by \log(1.3).

$$x=\frac{\log(\frac{246}{11})}{\log(1.3)}$$

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

$$x=\log_{1.3}\left(\frac{246}{11}\right)$$

Solve for x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(1.3)}+\log_{1.3}\left(\frac{246}{11}\right)$$

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