Solve 21/10=(1+0.40)^x

$$\frac { 21 } { 10 } = ( 1 + 0.40 ) ^ { x }$$

Solve for x

$$x=\log_{1.4}\left(2.1\right)\approx 2.205047739$$

Steps Using Definition of Logarithm

Add 1 and 0.4 to get 1.4.

$$\frac{21}{10}=1.4^{x}$$

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

$$1.4^{x}=\frac{21}{10}$$

Take the logarithm of both sides of the equation.

$$\log(1.4^{x})=\log(\frac{21}{10})$$

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

$$x\log(1.4)=\log(\frac{21}{10})$$

Divide both sides by \log(1.4).

$$x=\frac{\log(\frac{21}{10})}{\log(1.4)}$$

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

$$x=\log_{1.4}\left(\frac{21}{10}\right)$$

Solve for x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(1.4)}+\log_{1.4}\left(2.1\right)$$

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