2⁴=2·2·2·2=16
3⁴=3·3·3·3=81
1) 9/4 - 15/12 = 9*3/12 - 15/12 = 27/12 - 15/12 = 12/12 = 1
<span>Часть С</span><span>9) </span><span>1) [(b0,5 + 3)2 - (b0,5 - 3)2 ] / [b*[(b0,5 + 3) * (b0,5 - 3) ] = [b + 6b0,5 + 3
- b + 6b0,5 – 3] / b*(b – 9) = </span><span><span>= 12b0,5
/ b*(b – 9) = 12/</span>√b(b – 9) </span><span>2) [12/b0,5(b – 9)] * (b – 9)/b0,5
= 12 / b</span>
<span><span>10) </span>√<span>(9x2 – 6x + 1) = x2 + 1</span></span><span>(√<span>(9x2 – 6x + 1) )2
= (x2 + 1)2</span></span><span>9x2
– 6x + 1 = x4 + 2x2 + 1</span><span>x4
- 7x2 + 6x = 0</span><span>x(x3
– 7x + 6) = 0</span><span>x1
= 0</span><span>x3
– 7x + 6 = 0</span><span>x2
= 1</span><span> x3 – 7x +
6 <u>Ix
- 1
-(x3 – x2</u>) x2
+ x - 6
x2 – 7x
<u>-(x2 – x)</u>
- 6x + 6
<u>-(-6x + 6)
</u> 0</span><span>x3
– 7x + 6 = ( x – 1)( x2 + x – 6)</span><span> x2 + x – 6 = 0</span><span>x4 = 2</span><span>Ответ: x1 = 0; x2 = 1; x3 =
- 3; x4 = 2</span>
<span> </span>
1) lg5+lg2=lg5·2=lg10=1
2)log12 2+log12 72=log12( 2·72)=log12 144=log12 (12)²=2log12 12=2
3)log2 15-log2 (15\16)=log2 (15:15\16)=log2 (15·16\15)=log2 (16)=log2 (2)^4=4log2 2=4
4)log13 (169^1\5)=1\5log13 (13)²=2\5log13(13)=2\5
5) log(1\3) (243)^1\4=-1\4log3 (3)^5=-5\4log3 3=-5\4
6)lg8+lg125=lg(8·125)=lg1000=lg10³=3lg10=3
7)log3 6+log3 (3\2)=log3 (6·3\2)=log3 9=log3 (3)²=2log3( 3)=2
8)log5 75-log5 3=log5 (75\3)=log5 25=log5 (5)²=2log5 5=2
9)log8 (1\16)-log8 (32)=log8 (1\16:32)=log2³ (1\(2^9)=1\3log2 (2^-9)=-3log2 2=-3
10)log11 ∛121=log11 (∛11²)=2\3log11 11=2\3
11)log2(1\(128)^1\6)=log2 (2)^(-7\6)=-7\6log2 2=-7\6