Solve 14^3x+5=(1/14)

$$14 ^ { 3 x + 5 } = ( \frac { 1 } { 14 } )$$

Solve for x

$$x=-2$$

Steps Using Definition of Logarithm

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

$$14^{3x+5}=\frac{1}{14}$$

Take the logarithm of both sides of the equation.

$$\log(14^{3x+5})=\log(\frac{1}{14})$$

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

$$\left(3x+5\right)\log(14)=\log(\frac{1}{14})$$

Divide both sides by \log(14).

$$3x+5=\frac{\log(\frac{1}{14})}{\log(14)}$$

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

$$3x+5=\log_{14}\left(\frac{1}{14}\right)$$

Subtract 5 from both sides of the equation.

$$3x=-1-5$$

Divide both sides by 3.

$$x=-\frac{6}{3}$$

Solve for x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{3\ln(14)}-2$$

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