How to solve 49 ^ x = 7 ^ 3

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve 49 ^ x = 7 ^ 3 | Equatix

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$$49^{x}=7^{3}$$

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

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

$$49^{x}=343$$

Take the logarithm of both sides of the equation.

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

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

$$x\log(49)=\log(343)$$

Divide both sides by $\log(49)$.

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

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

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

$x=\frac{\pi n_{1}i}{\ln(7)}+\frac{3}{2}$
$n_{1}\in \mathrm{Z}$