exercise:D4d07d1b5a: Difference between revisions
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Assume that <math>a_1 > a_2 > 1</math>. | Assume that <math>a_1 > a_2 > 1</math>. | ||
<ul style{{=}}"list-style-type:lower-alpha" | <ul style{{=}}"list-style-type:lower-alpha"> | ||
<li> | <li>Using the definition of <math>a^x</math>, | ||
Using the definition of <math>a^x</math>, | |||
show that, if <math>x > 0</math>, then <math>{a_1}^x > {a_2}^x</math>.</li> | show that, if <math>x > 0</math>, then <math>{a_1}^x > {a_2}^x</math>.</li> | ||
<li>Using | <li>Using (a), show that, if <math>x < 0</math>, then <math>{a_1}^x < {a_2}^x</math>.</li> | ||
then <math>{a_1}^x < {a_2}^x</math>.</li> | |||
</ul> | </ul> | ||
Latest revision as of 23:39, 23 November 2024
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[/math]
Assume that [math]a_1 \gt a_2 \gt 1[/math].
- Using the definition of [math]a^x[/math], show that, if [math]x \gt 0[/math], then [math]{a_1}^x \gt {a_2}^x[/math].
- Using (a), show that, if [math]x \lt 0[/math], then [math]{a_1}^x \lt {a_2}^x[/math].