(2^x)^2<= 15^x

解答

(2^{x})^{2} \leq 1 5^{x}

x \geq \frac{2 ln ( 2 ) a _{4}}{ln ( 15 )}

求解步骤

(2^{x})^{2} \leq 1 5^{x}

若

f (x) \leq g (x)

，则

ln (f (x)) \leq ln (g (x))

ln ((2^{a_{4}})^{2}) \leq ln (1 5^{x})

化简

ln ((2^{a_{4}})^{2}) : 2 ln (2) a_{4}

化简

ln (1 5^{x}) : ln (15) x

2 ln (2) a_{4} \leq ln (15) x

2 ln (2) a_{4} \leq ln (15) x : x \geq \frac{2 ln ( 2 ) a _{4}}{ln ( 15 )}

x \geq \frac{2 ln ( 2 ) a _{4}}{ln ( 15 )}

\frac{1}{2 ^{x} - 1} > \frac{1}{1 - 2 ^{x - 1}}

((\frac{3}{7})^{x})^{2} < (\frac{7}{3})^{4} x - 2

(\frac{2}{5})^{\frac{( 1 - 5 x )}{( 4 + 16 )}} < \frac{25}{4}

4^{x - 1} + 2^{x + 1} \geq 2^{5}

2^{x + 2} > (\frac{1}{4})^{\frac{1}{x}}