Solve 3^4-2x=1/16

$$3 ^ { 4 - 2 x } = \frac { 1 } { 16 }$$

Solve for x

$$x=2\left(\log_{3}\left(2\right)+1\right)\approx 3.261859507$$

Steps Using Definition of Logarithm

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

$$3^{-2x+4}=\frac{1}{16}$$

Take the logarithm of both sides of the equation.

$$\log(3^{-2x+4})=\log(\frac{1}{16})$$

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

$$\left(-2x+4\right)\log(3)=\log(\frac{1}{16})$$

Divide both sides by \log(3).

$$-2x+4=\frac{\log(\frac{1}{16})}{\log(3)}$$

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

$$-2x+4=\log_{3}\left(\frac{1}{16}\right)$$

Subtract 4 from both sides of the equation.

$$-2x=-4\log_{3}\left(2\right)-4$$

Divide both sides by -2.

$$x=\frac{-4\log_{3}\left(2\right)-4}{-2}$$