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\(\Leftrightarrow3^x=5.3^{12}+4.\left(3^3\right)^4=5.3^{12}+4.3^{12}.\)
\(\Leftrightarrow3^x=9.3^{12}=3^2.3^{12}=3^{14}\Leftrightarrow x=14\)
a) \(x^{20}=x\)
\(\Rightarrow\orbr{\begin{cases}x=0\\x=1\end{cases}}\)
b) \(x^6:x^3=125\)
\(\Leftrightarrow x^{6-3}=125\)
\(\Leftrightarrow x^3=125\)
\(\Leftrightarrow x^3=5^3\)
\(\Leftrightarrow x=5\)
c) \(4x^3+12=120\)
\(\Leftrightarrow4x^3=120-12\)
\(\Leftrightarrow4x^3=108\)
\(\Leftrightarrow x^3=27\)
\(\Leftrightarrow x^3=3^3\)
\(\Leftrightarrow x=3\)
d) \(x^{10}=x^1\)
\(\Leftrightarrow x^{10}=x\)
\(\Rightarrow\orbr{\begin{cases}x=1\\x=0\end{cases}}\)
e) \(\left(2x-15\right)^5=\left(2x-15\right)^3\)
\(\Leftrightarrow\left(2x-15\right)^5-\left(2x-15\right)^3=0\)
\(\Leftrightarrow\left(2x-15\right)^3\left[\left(2x-15\right)^2-1\right]=0\)
\(\Rightarrow\orbr{\begin{cases}\left(2x-15\right)^3=0\\\left(2x-15\right)^2-1=0\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}2x-15=0\\\orbr{\begin{cases}2x-15=1\\2x-15=-1\end{cases}}\end{cases}}\Rightarrow\orbr{\begin{cases}x=\frac{15}{2}\\\orbr{\begin{cases}x=8\\x=-7\end{cases}}\end{cases}}\)\(\Rightarrow2x-15=0\)hoặc \(2x-15=1\) hoặc \(2x-15=-1\)
\(\Rightarrow x=\frac{15}{2}\)hoặc \(x=8\)hoặc \(x=7\)
\(a,2.3^x=10.3^{12}+8.27^4\)
\(\Leftrightarrow2.3^x=3^{12}\left(10+8\right)\)
\(\Leftrightarrow2.3^x=3^{12}.18\)
\(\Leftrightarrow2.3^x=3^{12}.3^2.2\)
\(\Leftrightarrow2.3^x=2.3^{14}\)
\(\Rightarrow3^x=3^{14}\)
\(\Rightarrow x=14\)
\(b,2^{4x}.3^6=12^6\)
\(\Leftrightarrow2^{4x}.3^6=2^{12}.3^6\)
\(\Rightarrow2^{4x}=2^{12}\)
\(\Rightarrow4x=12\)
\(\Rightarrow x=3\)
a :
[( 10 - x ) . 2 + 5] : 3 - 2 = 3
( 10 - x ) x 2 + 5 = ( 3+2) x 3
( 10 - x ) x 2 + 5 = 15
10 -x = ( 15 -5 ) : 2
10 - x = 5
x = 5
a) \(\left[\left(10-x\right)2+5\right]:3-2=3\)
\(\left(20-2x+5\right):3-2=3\)
\(\left(20-2x+5\right):3=5\)
\(20-2x+5=15\)
\(20-2x=10\)
\(2x=10\)
\(x=5\)
b) \(6x-302=2^3\cdot5\)
\(6x=8\cdot5+302\)
\(6x=342\)
\(x=57\)
c) \(12\left(x-1\right):3=4^3-2^3\)
\(12\left(x-1\right):3=56\)
\(12\left(x-1\right)=168\)
\(x-1=12\)
\(x=13\)
a, 5 . ( x - 6 ) - 415 = 15
5 . ( x -6 ) = 15 + 415
5 . ( x - 6 ) = 430
x-6 = 430 : 5
x - 6 = 86
x = 86 + 6
x = 92
b, ( 3 . x - 12 ) . 3 = \(3^3\)
3 . x - 12 = 27 : 3
3 . x - 12 = 9
3. x = 9 + 12
3 . x = 21
x = 21 : 3
x = 7
x, \(\left(5-x\right)^2\) . \(2^2\) = 64
\(\left(5-x\right)^2\) . 4 = 64
\(\left(5-x\right)^2\) = 64 : 4
\(\left(5-x\right)^2\) = 16
\(\left(5-x\right)^2\) = \(4^2\)
5 - x = 4
x = 5 -4
x =1
Tk mk nha
Bài 1:
a) \(x^{10}=1^x\Rightarrow\orbr{\begin{cases}x=1\\x=10\end{cases}}\)
b) \(x^{10}=x\Rightarrow x=1\)
c) \(\left(2x-15\right)^5=\left(2x-15\right)^3\)
\(\left(2x-15\right)^5.\left(2x-15\right)^3=\left(2x-15\right)^3\)
\(\left(2x-15\right)^2=1\Rightarrow x=8\)
Bài 2:
\(a;2^{16}=2^{13}\cdot2^3=2^{13}\cdot8>7\cdot2^{13}\)
\(b;49^8\cdot27^5=7^{16}\cdot3^{15}=21^{15}\cdot7>21^5\)
C;Ta có:\(199^{20}< 200^{20}=2^{20}\cdot10^{40}=2^{15}\cdot10^{40}\cdot2^5\)
\(2003^{15}>2000^{15}=2^{15}\cdot10^{45}=2^{15}\cdot10^{40}\cdot10^5\)
Vì 25<105 nên 19920<200315
\(d;3^{39}< 3^{40}=9^{20}< 11^{20}< 11^{21}\)
Xét vế trái của biểu thức (VT)
\(VT=1+2^2\left(1+1\right)+3^2\left(2+1\right)+4^2\left(3+1\right)+...+10^2\left(9+1\right)\)
\(VT=1+1.2^2+2^2+2.3^2+3^2+3.4^2+4^2+...+9.10^2+10^2\)
\(VT=\left(1+2^2+3^2+4^2+...+10^2\right)+\left(1.2^2+2.3^2+3.4^2+...+9.10^2\right)\)
Đặt \(A=1+2^2+3^2+4^2+...+10^2\)
\(A=1+2\left(1+1\right)+3\left(2+1\right)+4\left(3+1\right)+...+10\left(9+1\right)\)
\(A=1+1.2+2+2.3+3+3.4+4+...+9.10+10\)
\(A=\left(1+2+3+4+...+10\right)+\left(1.2+2.3+3.4+...+9.10\right)\)
Đặt \(B=1.2^2+2.3^2+3.4^2+...+9.10^2\)
\(B=1.2\left(3-1\right)+2.3\left(4-1\right)+3.4\left(5-1\right)+...+9.10\left(11-1\right)\)
\(B=1.2.3-1.2+2.3.4-2.3+3.4.5-3.4+...+9.10.11-9.10\)
\(B=\left(1.2.3+2.3.4+3.4.5+...+9.10.11\right)-\left(1.2+2.3+3.4+...+9.10\right)\)
\(VT=A+B=\left(1+2+3+4+...+10\right)+\left(1.2.3+2.3.4+3.4.5+...+9.10.11\right)\)
Đặt \(C=1+2+3+4+...+10=55\) (Tổng cấp số cộng)
Đặt \(D=1.2.3+2.3.4+3.4.5+...+9.10.11\)
\(4D=1.2.3.4+2.3.4.4+3.4.5.4+...+9.10.11.4\)
\(4D=1.2.3.4+2.3.4\left(5-1\right)+3.4.5\left(6-2\right)+...+9.10.11\left(12-8\right)\)
\(4D=1.2.3.4-1.2.3.4+2.3.4.5-2.3.4.5+3.4.5.6-...-8.9.10.11+9.10.11.12\)
\(4D=9.10.11.12\Rightarrow D=3.9.10.11\)
\(\Rightarrow VT=C+D=55+3.9.10.11=3025=55^2\)
\(\Rightarrow55^2=\left(x+1\right)^2\Rightarrow55=x+1\Rightarrow x=54\)
2.3x = 10.312 + 8.312
2.3x = (10+8).312
2.3x = 18.312
2.3x = 2.32.312
2.3x = 2.314
=> x = 14
2.3^x=10.3^12+8.3^12
2.3^x=3^12.(10+8)
2.3^x=3^12.18
2.3^x=3^12.(3^2+3^2)
2.3^x=3^12.3^2+3^12.3^2
2.3^x=3^15+3^15
2.3^x=3^15.2
=> 3^x=3^15
=> x=15