Solve 3*4^2k+8=24

$$3 \times 4 ^ { 2 k + 8 } = 24$$

Solve for k

$$k = -\frac{13}{4} = -3\frac{1}{4} = -3.25$$

Steps Using Definition of Logarithm

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

$$3\times 4^{2k+8}=24$$

Divide both sides by 3.

$$4^{2k+8}=8$$

Take the logarithm of both sides of the equation.

$$\log(4^{2k+8})=\log(8)$$

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

$$\left(2k+8\right)\log(4)=\log(8)$$

Divide both sides by \log(4).

$$2k+8=\frac{\log(8)}{\log(4)}$$

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

$$2k+8=\log_{4}\left(8\right)$$

Subtract 8 from both sides of the equation.

$$2k=\frac{3}{2}-8$$

Divide both sides by 2.

$$k=-\frac{\frac{13}{2}}{2}$$

Solve for k (complex solution)

$$k=\frac{\pi n_{1}i}{2\ln(2)}-\frac{13}{4}$$

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