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\(\frac{11.3^{22}.3^7-\left(3^2\right)^{15}}{2^2.3^{28}}=\frac{11.3^{29}-3^{30}}{2^2.3^{28}}=\frac{3^{29}.\left(11-3\right)}{2^2.3^{28}}=\frac{3^{29}.2^3}{2^2.3^{28}}=3.2=6\)
\(\frac{11.3^{22}.3^7-9^{15}}{\left(2.3^{14}\right)^2}\)
\(=\frac{11.3^{22}.3^7-\left(3^2\right)^{15}}{\left(2.3^{14}\right)^2}\)
\(=\frac{11.3^{22}.3^7-3^{30}}{\left(2.3^{14}\right)^2}\)
\(=\frac{11.3^{29}-3^{30}}{\left(2.3^{14}\right)^2}\)
\(=\frac{11.3^{29}-3^{30}}{2^2.3^{28}}\)
\(=\frac{11.3^{29}-3.3^{29}}{4.3^{28}}\)
\(=\frac{\left(11-3\right).3^{29}}{4.3^{28}}\)
\(=\frac{8.3^{29}}{4.3^{28}}\)
\(=2.3=6\)
A = 12 : {390 : [500 - (125 + 35.7)]}
A = 12 : {390 : [500 - (125 + 245)]}
A = 12 : {390 : [500 - 370]}
A = 12 : {390 : 130}
A = 12 : 3 = 4
B = 12000 - (1500 . 2 + 1800.3 + 1800.2 : 3)
B = 12000 - (3000 + 5400 + 1200)
B = 12000 - 9600 = 2400
C = \(\frac{11\cdot3^{22}\cdot3^7-9^{15}}{\left(2\cdot3^{14}\right)^2}=\frac{11\cdot3^{22}\cdot3^7-\left(3^2\right)^{15}}{2^2\cdot3^{28}}=\frac{11\cdot3^{29}-3^{30}}{2^2\cdot3^{28}}=\frac{11\cdot3\cdot3^{28}-3^2\cdot3^{28}}{2^2\cdot3^{28}}\)
\(=\frac{33\cdot3^{28}-9\cdot3^{28}}{4\cdot3^{28}}=\frac{\left(33-9\right)\cdot3^{28}}{4\cdot3^{28}}=\frac{24}{4}=6\)
3^(x-1)+2.3^(x+1)=19
3^[x+1+(-2)]+2.3^(x+1)=19
3^(x+1).3^(-2)+2.3^(x+1)=19
3^(x+1).[3^(-2)+2]=19
3^(x+1).19/9=19
3^(x+1)=3^2
x+1=2
x=1
\(2.3^{x+2}=54\)
\(\Leftrightarrow3^{x+2}=27\)
\(\Leftrightarrow3^{x+2}=3^3\)
\(\Leftrightarrow x+2=3\)
\(\Leftrightarrow x=1\)
2.3^x+2 = 54
3^x+2 = 54 : 2 = 27
3^x+2 = 3^3
=> x + 2 = 3
x = 3 - 2 = 1