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2.3x= 10.312+8.274
2.3x = 10.(33)4+ (33)4 . 8
2.3x= (33)4. 18
2.3x= (33)4.2.32
2.3x= 312+2.2
2.3x= 314.2
=> x = 14
1/ a) \(2.3.12.12.3=2.3.2^2.3.2^2.3.3=2^5.3^4\)
b) \(3.5.27.125=3.5.3^3.5^3=3^4.5^4=\left(3.5\right)^4\)
2/ a) \(\left(27^3\right)^4=27^{3.4}=27^{12}\)
Vậy \(\left(27^3\right)^4=27^{12}\)
b) \(5^{36}=\left(5^6\right)^6\) và \(11^{24}=\left(11^4\right)^6\)
Do đó \(5^6=15625\) và \(11^4=14641\)
Vì 15625>14641 nên\(\left(5^6\right)^6>\left(11^4\right)^6hay5^{36}>11^{24}.\)
3/ a) \(x^3=125=>x=5\)
b) \(\left(3x-14\right)^3=2^5.5^2+200\)
\(\left(3x-14\right)^3=1000\)
\(3x-14=10^3\)
\(3x=10^3+14\)
\(3x=1014\)
\(x=\frac{1014}{3}=338\)
c) \(\left(2x-1\right)^4=81\)
\(\left(2x-1\right)^4=3^4\)
\(2x-1=3\)
\(2x=3+1\)
\(x=\frac{4}{2}=2\)
d) \(5x+3^4=2^2.7^2\)
\(5x+3^4=\left(2.7\right)^2=14^2\)
\(5x+81=196\)
\(5x=196-81\)
\(5x=115\)
\(x=\frac{115}{5}=23\)
e) \(4^x=1024=>x=5\).
Đề bài bạn 3 câu sai nha !
\(a,\text{ }3^x=34\)
\(\Rightarrow\text{ }x\in\varnothing\)
\(b,\text{ }2^{2x-3}=29\)
\(\Rightarrow\text{ }x\in\varnothing\)
\(c,\text{ }2^x=64\)
\(2^x=2^6\)
\(\Rightarrow\text{ }x=6\)
\(d,\text{ }x^2=16\)
\(x^2=\left(\pm4\right)^2\)
\(x=\pm4\)
\(e,\text{ }15^x=34\)
\(x\in\varnothing\)
Bạn viết nhầm đề à ?
\(a,\text{ }3^x=34\)
\(\Rightarrow\text{ }x\in\varnothing\)
\(b,\text{ }2^{2x-3}=29\)
\(\Rightarrow\text{ }x\in\varnothing\)
\(c,\text{ }2^x=64\)
\(2^x=2^6\)
\(\Rightarrow\text{ }x=6\)
\(d,\text{ }x^2=16\)
\(x^2=\left(\pm4\right)^2\)
\(x=\pm4\)
\(e,\text{ }15^x=34\)
\(x\in\varnothing\)
a)|x-3|=7-(-2)
|x-3|=9
x-3=9
th1:x-3=9 th2:x-3=-9
x=9+3=12 x=(-9)+3=-6
b. ( 7-x ) - ( 25+7) = -25 c. (3x - 2 mũ 4 ) . 7 mũ 3 = 2. 7 mũ 4
7-x-25-7=-25 3x-2^4=2.7^4:7^3
-x-25=-25 3x-16=14
-x=0 3x=30
vậy x=0 vậy x=10
\(a=2^1+2^2+2^3+...+2^{100}\)
\(2a=2^2+2^3+2^4+...+2^{101}\)
\(2a-a=\left(2^2+2^3+2^4+...+2^{101}\right)-\left(2^1+2^2+2^3+...+2^{100}\right)\)
\(a=2^{101}-2\)
\(a+2=2^{101}-2+2=2^{201}\)
\(\Rightarrow x=101\)
\(a=2^1+2^2+2^3+...+2^{100}\)
\(2a=2^2+2^3+2^4+...+2^{99}+2^{100}\)
\(2a-a=\left(2^2+2^3+2^4+...+2^{99}+2^{100}\right)-\left(2^1+2^2+2^3+...+2^{100}\right)\)
\(a=2^{99}-2\)
\(a+2=2^{99}-2+2=2^{99}\)
\(\Rightarrow x=99\)
tìm x E Z biết
a, 0 : x =0
\(\Rightarrow x=\frac{0}{0}\)
\(\Rightarrow x\in\varnothing\)
b, 4 mũ x =64
\(\Rightarrow4^x=4^3\)
\(\Rightarrow x=3\)
c, 2 mũ x =16
\(\Rightarrow2^x=2^4\)
\(\Rightarrow x=4\)
d, 9 mũ x-1=9
\(\Rightarrow x-1=1\)
\(\Rightarrow x=2\)
e,x mũ 4 =16
\(\Rightarrow x^4=2^4\)
\(\Rightarrow x=2\)
g, 2 mũ x : 2 mũ 5 =1
\(\Rightarrow2^{x-5}=1\)
\(\Rightarrow x-5=0\)
\(\Rightarrow x=5\)
giúp mk với mk đang cần
+) \(x^3=x^2\Leftrightarrow\orbr{\begin{cases}x=0\\x=1\end{cases}}\)
+) \((7x-11)^3=2^5.5^2+200\)
\((7x-11)^3=2^3.2^2.5^2+2^3.5^2\)
\((7x-11)^3=2^3.5^2.(2^2+1)\)
\((7x-11)^3=2^3.5^2.5\)
\((7x-11)^3=2^3.5^3\)
\((7x-11)^3=10^3\)
\(\Rightarrow7x-11=10\)
\(7x=21\)
\(x=3\)
+) \(3+2^{x-1}=24-[4^2-(2^2-1)]\)
\(3+2^{x-1}=11\)
\(2^{x-1}=8\)
\(2^{x-1}=2^3\)
\(\Rightarrow x-1=3\)
\(x=4\)