Solve 2^30k+6=2.4

$$2 ^ { 30 k + 6 } = 2.4$$

Solve for k

$$k=\frac{\log_{2}\left(0.6\right)}{30}-\frac{2}{15}\approx -0.157898853$$

Steps Using Definition of Logarithm

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

$$2^{30k+6}=2.4$$

Take the logarithm of both sides of the equation.

$$\log(2^{30k+6})=\log(2.4)$$

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

$$\left(30k+6\right)\log(2)=\log(2.4)$$

Divide both sides by \log(2).

$$30k+6=\frac{\log(2.4)}{\log(2)}$$

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

$$30k+6=\log_{2}\left(2.4\right)$$

Subtract 6 from both sides of the equation.

$$30k=\frac{\ln(\frac{12}{5})}{\ln(2)}-6$$

Divide both sides by 30.

$$k=\frac{\frac{\ln(\frac{12}{5})}{\ln(2)}-6}{30}$$