Tìm x:
1) \(2\cdot3^x=10\cdot3^{12}+8\cdot27^4\)
2) \(\left(19x+2\cdot5^2\right):14=\left(13-8\right)^2-4^2\)
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1) ( 2x -15 )5 = ( 2x - 15 )3
( 2x -15 )5 - ( 2x - 15 )3 = 0
( 2x - 15 )3 . [ ( 2x - 15 )2 - 1 ] = 0
\(\orbr{\begin{cases}\left(2x-15\right)^3=0\\\left(2x-15\right)^2-1=0\end{cases}}\)
\(\orbr{\begin{cases}2x-15=0\\2x-15=1\end{cases}}\)
\(\orbr{\begin{cases}2x=15\\2x=16\end{cases}}\)
\(\orbr{\begin{cases}x=\frac{15}{2}\\x=8\end{cases}}\)
a) \(2^x+5=21\)
\(\Rightarrow2^x=21-5=16\Rightarrow2^x=2^4\)
Vậy x = 4
b) \(2^x-1+3^2=5^2+2.5\)
\(\Rightarrow2^x-1+9=35\)
\(\Rightarrow2^x=35-9+1=27\)
Vậy x không có giá trị
c;d;e;f làm tương tự
\(a,\left(19x+2.5^2\right):14=\left(13-8\right)^2-4^2\)
\(\Leftrightarrow\left(19x+50\right):14=5^2-4^2\)
\(\Leftrightarrow\left(19x+50\right):14=9\)
\(\Leftrightarrow19x+50=126\)
\(\Leftrightarrow19x=76\Leftrightarrow x=4\)
b) x + ( x + 1 ) + ( x + 2 ) + ... + ( x + 30 ) = 1240
x + x + 1 + x + 2 + ... + x + 30 = 1240
( x + x + ... + x ) + ( 1 + 2 + ... + 30 ) = 1240
Số số hạng là : ( 30 - 1 ) : 1 + 1 = 30 ( số )
Tổng là : ( 30 + 1 ) . 30 : 2 = 465
=> 31x + 465 = 1240
=> 31x = 775
=> x = 25
Vậy........
\(15-\left\{2.\left[\left(2x-4\right).5\right].3.\left(x+1\right)\right\}=12-x\)
\(15-\left\{\left[10x-20\right].6.\left(x+1\right)\right\}=12-x\)
\(15-\left\{10x-20.6x+1\right\}=12-x\)
\(15-\left\{10x-120x+1\right\}=12-x\)
\(15-\left(-110x\right)-1=12-x\)
\(15+110x-1=12-x\)
\(110x+x=12-15+1\)
\(111x=-2\)
\(x=\dfrac{-2}{111}\)
a) \(2^x+5=21\)
\(2^x=21-5\)
\(2^x=16\)
\(2^x=2^4\)
\(\Rightarrow x=4\)
Vậy \(x=4\)
a ) \(2^x+5=21\)
\(2^x=21-5\)
\(2^x=16\)
\(2^x=2^4\)
\(\Rightarrow x=4\)
\(B=\frac{2^{12}.3^5-4^6.9^2}{\left(2^2.3\right)^6+8^4.3^5}-\frac{5^{10}.7^3-25^5.49^2}{\left(125.7\right)^3+5^9.14^3}\)
\(B=\frac{2^{12}.3^6-2^{12}.3^4}{2^{12}.3^6+2^{12}.3^5}-\frac{5^{10}.7^3-5^{10}.7^4}{5^9.7^3+5^9.2^3.7^3}\)
\(B=\frac{2^{12}.3^4.\left(3^2-1\right)}{2^{12}.3^5.\left(3-1\right)}-\frac{5^{10}.7^3.\left(1-7\right)}{5^9.7^3.\left(1+2^3\right)}\)
\(B=\frac{8}{6}-\frac{5-35}{9}\)
\(B=\frac{4}{3}+\frac{30}{9}\)
\(B=\frac{4}{3}+\frac{10}{3}\)
\(B=\frac{14}{3}\)
vậy \(B=\frac{14}{3}\)
\(2.3^x=10.3^{12}+8.27^4\)
\(2.3^x=10.531441+8.531441\)
\(2.3^x=\left(10+8\right).531441\)
\(2.3^x=18.531441\)
\(2.3^x=9565938\)
\(3^x=9565938:2\)
\(3^x=4782969\)
\(3^x=3^{14}\)
\(\Rightarrow x=14\)
Thanks!