Solve -6*2^0.1x=-100

$$- 6 \cdot 2 ^ { 0.1 x } = - 100$$

Solve for x

$$x=\log_{2}\left(\frac{95367431640625}{59049}\right)+10\approx 40.588936891$$

Steps Using Definition of Logarithm

Divide both sides by -6.

$$2^{0.1x}=\frac{-100}{-6}$$

Reduce the fraction \frac{-100}{-6} to lowest terms by extracting and canceling out -2.

$$2^{0.1x}=\frac{50}{3}$$

Take the logarithm of both sides of the equation.

$$\log(2^{0.1x})=\log(\frac{50}{3})$$

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

$$0.1x\log(2)=\log(\frac{50}{3})$$

Divide both sides by \log(2).

$$0.1x=\frac{\log(\frac{50}{3})}{\log(2)}$$

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

$$0.1x=\log_{2}\left(\frac{50}{3}\right)$$

Multiply both sides by 10.

$$x=\frac{\ln(\frac{50}{3})}{0.1\ln(2)}$$

Solve for x (complex solution)

$$x=\frac{i\times 20\pi n_{1}}{\ln(2)}+\log_{2}\left(\frac{95367431640625}{59049}\right)+10$$

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