Solve 128*1.5^x=17180000

$$128 \times { 1.5 }^{ x } =17180000$$

Solve for x

$$x=\log_{1.5}\left(134218.75\right)\approx 29.120202884$$

Steps Using Definition of Logarithm

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

$$128\times 1.5^{x}=17180000$$

Divide both sides by 128.

$$1.5^{x}=\frac{536875}{4}$$

Take the logarithm of both sides of the equation.

$$\log(1.5^{x})=\log(\frac{536875}{4})$$

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

$$x\log(1.5)=\log(\frac{536875}{4})$$

Divide both sides by \log(1.5).

$$x=\frac{\log(\frac{536875}{4})}{\log(1.5)}$$

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

$$x=\log_{1.5}\left(\frac{536875}{4}\right)$$

Solve for x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(1.5)}+\log_{1.5}\left(134218.75\right)$$

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