Solve 1.5*(1.07)^x=4

$$1.5 \times ( 1.07 ) ^ { x } = 4$$

Solve for x

$$x=\log_{1.07}\left(\frac{8}{3}\right)\approx 14.496731388$$

Steps Using Definition of Logarithm

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

$$1.5\times 1.07^{x}=4$$

Divide both sides of the equation by 1.5, which is the same as multiplying both sides by the reciprocal of the fraction.

$$1.07^{x}=\frac{8}{3}$$

Take the logarithm of both sides of the equation.

$$\log(1.07^{x})=\log(\frac{8}{3})$$

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

$$x\log(1.07)=\log(\frac{8}{3})$$

Divide both sides by \log(1.07).

$$x=\frac{\log(\frac{8}{3})}{\log(1.07)}$$

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

$$x=\log_{1.07}\left(\frac{8}{3}\right)$$

Solve for x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(1.07)}+\log_{1.07}\left(\frac{8}{3}\right)$$

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