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<b>let </b><font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c2">b</font>, <font color="Maroon" title="c3">c</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c3">c</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c3">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 implies <font color="Maroon" title="c1">a</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <font color="Maroon" title="c2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">b</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c1">a</font></span>)</span></span>)</span> )</span><br/>

<b>assume </b><b>that </b><br/><a NAME="E1:7"/><i><font color="Green" title="E5">A1</font></i>: 
<font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>and </b><br/><a NAME="E2:7"/><i><font color="Green" title="E6">A2</font></i>: 
<font color="Maroon" title="c3">c</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>and </b><br/><a NAME="E3:7"/><i><font color="Green" title="E7">A3</font></i>: 
<font color="Maroon" title="c3">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">a</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <font color="Maroon" title="c2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">b</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c1">a</font></span>)</span></span>)</span></span><br/>

<a NAME="E4:7"/><i><font color="Green" title="E8">A4</font></i>: 
<font color="Maroon" title="c1">a</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <font color="Maroon" title="c2">b</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="txt" href="asympt_1.html#E1:7"><i><font color="Green" title="E5">A1</font></i></a>, <a class="ref" href="power.html#T39" title="POWER:th.39">POWER:39</a></i>;<br/>
<a NAME="E5:7"/>
 <a href="power.html#K6" title="POWER:func.6">log</a> <font color="Maroon" title="c3">c</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">b</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c1">a</font></span>)</span>
 
<b>by </b><i><a class="txt" href="asympt_1.html#E1:7"><i><font color="Green" title="E5">A1</font></i></a>, <a class="txt" href="asympt_1.html#E2:7"><i><font color="Green" title="E6">A2</font></i></a>, <a class="txt" href="asympt_1.html#E3:7"><i><font color="Green" title="E7">A3</font></i></a>, <a class="ref" href="power.html#T63" title="POWER:th.63">POWER:63</a></i>;<br/>
<b>hence </b><a NAME="E6:7"/>
<font color="Maroon" title="c1">a</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <font color="Maroon" title="c2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">b</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c1">a</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="asympt_1.html#E2:7"><i><font color="Green" title="E6">A2</font></i></a>, <a class="txt" href="asympt_1.html#E3:7"><i><font color="Green" title="E7">A3</font></i></a>, <a class="txt" href="asympt_1.html#E4:7"><i><font color="Green" title="E8">A4</font></i></a>, <a class="ref" href="power.html#D3" title="POWER:def.3">POWER:def 3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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