Solve 34^x=16

$${ 34 }^{ x } = 16$$

Solve for x

$$x=4\log_{34}\left(2\right)\approx 0.786246529$$

Steps Using Definition of Logarithm

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

$$34^{x}=16$$

Take the logarithm of both sides of the equation.

$$\log(34^{x})=\log(16)$$

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

$$x\log(34)=\log(16)$$

Divide both sides by \log(34).

$$x=\frac{\log(16)}{\log(34)}$$

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

$$x=\log_{34}\left(16\right)$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(34)}+4\log_{34}\left(2\right)$$

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