Solve 343*49^x=1

$$343 \times 49 ^ { x } = 1$$

Solve for x

$$x = -\frac{3}{2} = -1\frac{1}{2} = -1.5$$

Steps Using Definition of Logarithm

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

$$343\times 49^{x}=1$$

Divide both sides by 343.

$$49^{x}=\frac{1}{343}$$

Take the logarithm of both sides of the equation.

$$\log(49^{x})=\log(\frac{1}{343})$$

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

$$x\log(49)=\log(\frac{1}{343})$$

Divide both sides by \log(49).

$$x=\frac{\log(\frac{1}{343})}{\log(49)}$$

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

$$x=\log_{49}\left(\frac{1}{343}\right)$$

Solve for x (complex solution)

$$x=\frac{\pi n_{1}i}{\ln(7)}-\frac{3}{2}$$

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