<span>6^lgx=72-x^lg6 ;
</span>6^lgx +x^lg6=72 ; * * * x^lg6 = 6^lgx _правила <span>перекладина</span> * * *
<span>2*(6^lgx) =72 ;
</span>(6^lgx) =6² ;
lgx =2⇒ <span>x=100.
</span>
ответ : 100 .
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(Log_b c) *(Log_b a) =(Log_b a)*(Log_b c )⇔
Log_b (a ^ Log_b c) = <span>Log_b (</span>c^ <span>Log_b a) </span>⇒a ^ Log_b c = c^ <span>Log_b a.</span>
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</span>
Пусть x км/ч - c<span>корость велосипедиста </span>
<span>Пусть y км /ч - скорость пешехода </span>
<span>x = 3*y </span>
<span>x = 8+y </span>
<span>3y = 8+y </span>
<span>(8+y)/y=3 </span>
<span>8/y+y/y=3 </span>
<span>1+8/y=3 </span>
<span>8/y=3-1 </span>
<span>8/y=2 </span>
<span>y=4 </span>
<span>x=3*y </span>
<span>x=12</span>
X²+3x-10/x+5
Запишем обычное деление столбиком:
x²+3x-10 / x+5
- _____
x²+5x / x-2
_______/
-2x-10/
- /
<span>-2x-10/
_______
0
Т.о. </span>x²+3x-10=(x+5)(x-2) => x²+3x-10/x+5=<span>(x+5)(x-2)/x+5=x-2</span>
X+8/5-5x+1/3=9
-4x=9-8/5-1/3
-4x=9-24/15-5/15
-4x=9-29/15
-4x=9-1_14/15
-4x=7_1/15
x= -106/15 * 1/4
x= - 53/15 * 1/2
x= - 53/30
x= -1_23/30