Solve 168^2+3x=1

$$16 { 8 }^{ 2+3x } =1$$

Solve for x

$$x = -\frac{10}{9} = -1\frac{1}{9} \approx -1.111111111$$

Steps Using Definition of Logarithm

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

$$16\times 8^{3x+2}=1$$

Divide both sides by 16.

$$8^{3x+2}=\frac{1}{16}$$

Take the logarithm of both sides of the equation.

$$\log(8^{3x+2})=\log(\frac{1}{16})$$

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

$$\left(3x+2\right)\log(8)=\log(\frac{1}{16})$$

Divide both sides by \log(8).

$$3x+2=\frac{\log(\frac{1}{16})}{\log(8)}$$

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

$$3x+2=\log_{8}\left(\frac{1}{16}\right)$$

Subtract 2 from both sides of the equation.

$$3x=-\frac{4}{3}-2$$

Divide both sides by 3.

$$x=-\frac{\frac{10}{3}}{3}$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{9\ln(2)}-\frac{10}{9}$$

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