Solve log_5 x^2 >=-7

Evaluate

lo g_{5} (x^{2}) \geq - 7

Find the domain

More Steps

lo g_{5} (x^{2}) \geq - 7, x \neq = 0

For 5 >1 the expression lo g_{5} (x^{2}) \geq - 7 is equivalent to x^{2} \geq 5^{- 7}

x^{2} \geq 5^{- 7}

Evaluate the power

x^{2} \geq \frac{1}{5 ^{7}}

Take the 2 -th root on both sides of the inequality

x^{2} \geq \frac{1}{5 ^{7}}

Calculate

∣ x ∣ \geq \frac{5}{625}

Separate the inequality into 2 possible cases

x \geq \frac{5}{625} x \leq - \frac{5}{625}

Find the union

x \in (- \infty, - \frac{5}{625}] \cup [\frac{5}{625}, + \infty)

Check if the solution is in the defined range

x \in (- \infty, - \frac{5}{625}] \cup [\frac{5}{625}, + \infty), x \neq = 0

Solution

x \in (- \infty, - \frac{5}{625}] \cup [\frac{5}{625}, + \infty)

Solve the inequality