Solve 7.49^x+2=49

$$7.49 ^ { x + 2 } = 49$$

Solve for x

$$x=-2\log_{7.49}\left(1.07\right)\approx -0.067202718$$

Steps Using Definition of Logarithm

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

$$7.49^{x+2}=49$$

Take the logarithm of both sides of the equation.

$$\log(7.49^{x+2})=\log(49)$$

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

$$\left(x+2\right)\log(7.49)=\log(49)$$

Divide both sides by \log(7.49).

$$x+2=\frac{\log(49)}{\log(7.49)}$$

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

$$x+2=\log_{7.49}\left(49\right)$$

Subtract 2 from both sides of the equation.

$$x=\frac{2\ln(7)}{\ln(\frac{749}{100})}-2$$

Solve for x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(7.49)}-2\log_{7.49}\left(1.07\right)$$

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