Solve 7^-x=49

$$7 ^ { - x } = 49$$

Solve for x

$$x=-2$$

Steps Using Definition of Logarithm

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

$$7^{-x}=49$$

Take the logarithm of both sides of the equation.

$$\log(7^{-x})=\log(49)$$

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

$$-x\log(7)=\log(49)$$

Divide both sides by \log(7).

$$-x=\frac{\log(49)}{\log(7)}$$

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

$$-x=\log_{7}\left(49\right)$$

Divide both sides by -1.

$$x=\frac{2}{-1}$$

Solve for x (complex solution)

$$x=-\frac{i\times 2\pi n_{1}}{\ln(7)}-2$$

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