Solve 384400=0.00001*2^x

$$384400 = 0.00001 \cdot 2 ^ { x }$$

Solve for x

$$x=\log_{2}\left(38440000000\right)\approx 35.161889285$$

Steps Using Definition of Logarithm

Divide both sides by 0.00001.

$$\frac{384400}{0.00001}=2^{x}$$

Expand \frac{384400}{0.00001} by multiplying both numerator and the denominator by 100000. Anything divided by one gives itself.

$$38440000000=2^{x}$$

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

$$2^{x}=38440000000$$

Take the logarithm of both sides of the equation.

$$\log(2^{x})=\log(38440000000)$$

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

$$x\log(2)=\log(38440000000)$$

Divide both sides by \log(2).

$$x=\frac{\log(38440000000)}{\log(2)}$$

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

$$x=\log_{2}\left(38440000000\right)$$

Solve for x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(2)}+\log_{2}\left(38440000000\right)$$

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