Solve inequalities of the form a^x > or < b Algebra II

Find the solution(s) to the following inequalities.

3^x≤31

x\leq\dfrac{\ln\left(3\right)}{\ln\left(31\right)}

x\geq\dfrac{\ln\left(31\right)}{\ln\left(3\right)}

x\leq\dfrac{\ln\left(31\right)}{\ln\left(3\right)}

x\geq\dfrac{\ln\left(3\right)}{\ln\left(31\right)}

5^x \gt 15

x \gt \dfrac{\ln\left(15\right)}{\ln\left(5\right)}

x \lt \dfrac{\ln\left(15\right)}{\ln\left(5\right)}

x \gt \dfrac{\ln\left(5\right)}{\ln\left(15\right)}

x \gt \ln\left(3\right)

2 \cdot 4^x \gt 6

x \gt \dfrac{\ln\left(3\right)}{\ln\left(4\right)}

x \lt \dfrac{\ln\left(3\right)}{\ln\left(4\right)}

x \gt \dfrac{\ln\left(6\right)}{\ln\left(8\right)}

x \gt \dfrac{\ln\left(6\right)}{2\ln\left(4\right)}

3^{6x} \geq 42

x \geq \dfrac{\ln\left(42\right)}{6\ln\left(3\right)}

x \geq \dfrac{\ln\left(7\right)}{\ln\left(3\right)}

x \leq \dfrac{\ln\left(42\right)}{\ln\left(18\right)}

x \leq \dfrac{\ln\left(42\right)}{6\ln\left(3\right)}

\left(7 \cdot 3^8\right)^x \lt 5

x \lt \dfrac{\ln\left(5\right)}{\ln\left(7 \cdot 3^8\right)}

x \lt \dfrac{\ln\left(5\right)}{8\ln\left(7 \cdot 3\right)}

x \gt \dfrac{8\ln\left(7 \cdot 3\right)}{\ln\left(5\right)}

x \gt \dfrac{\ln\left(7 \cdot 3^8\right)}{\ln\left(5\right)}

6^{\frac{-3}{2}x} \gt 3

x \lt \left(\dfrac{-2}{3}\right)\dfrac{\ln\left(3\right)}{\ln\left(6\right)}

x \lt \left(\dfrac{3}{2}\right)\dfrac{\ln\left(3\right)}{\ln\left(6\right)}

x \gt \dfrac{\ln\left(\dfrac{2}{3} \cdot 6\right)}{\ln\left(3\right)}

x \lt \left(\dfrac{-3}{2}\right)\dfrac{\ln\left(3\right)}{\ln\left(6\right)}

8^x \leq 145

x \leq \dfrac{\ln\left(145\right)}{\ln\left(8\right)}

x \geq \dfrac{\ln\left(8\right)}{\ln\left(145\right)}

x \geq \dfrac{\ln\left(145\right)}{\ln\left(8\right)}

x \leq \dfrac{\ln\left(8\right)}{\ln\left(145\right)}