Solve (1/16)^x-0.1=0.25

$$( \frac { 1 } { 16 } ) ^ { x - 0.1 } = 0.25$$

Solve for x

$$x=0.6$$

Steps Using Definition of Logarithm

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

$$\left(\frac{1}{16}\right)^{x-0.1}=0.25$$

Take the logarithm of both sides of the equation.

$$\log(\left(\frac{1}{16}\right)^{x-0.1})=\log(0.25)$$

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

$$\left(x-0.1\right)\log(\frac{1}{16})=\log(0.25)$$

Divide both sides by \log(\frac{1}{16}).

$$x-0.1=\frac{\log(0.25)}{\log(\frac{1}{16})}$$

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

$$x-0.1=\log_{\frac{1}{16}}\left(0.25\right)$$

Add 0.1 to both sides of the equation.

$$x=\frac{1}{2}-\left(-0.1\right)$$

Solve for x (complex solution)

$$x=-\frac{i\pi n_{1}}{2\ln(2)}+0.6$$

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