Bài 1:
a) \(\left(375-180\right):15\)
\(=195:15\)
\(=13\)
b) \(678\left(276+49\right)-678\left(149+76\right)\)
\(=678.325-678.225\)
\(=678\left(325-225\right)\)
\(=678.100\)
\(=67800\)
Bài 2:
\(12:\left\{390:\left[500-\left(125+35.7\right)\right]\right\}\)
\(=12:\left\{390:\left[500-\left(125+245\right)\right]\right\}\)
\(=12:\left\{390:\left[500-370\right]\right\}\)
\(=12:\left\{390:130\right\}\)
\(=12:3\)
\(=4\)
Bài 3:
a) \(2.3^x=54\)
\(\Leftrightarrow3^x=54:2\)
\(\Leftrightarrow3^x=27\)
\(\Leftrightarrow3^x=3^3\)
\(\Leftrightarrow x=3\)
b) \(3^2.3^x=81\)
\(\Leftrightarrow9.3^x=81\)
\(\Leftrightarrow3^x=81:9\)
\(\Leftrightarrow3^x=9\)
\(\Leftrightarrow3^x=3^2=\left(-3\right)^2\)
\(\Leftrightarrow x=2\)
c) \(\left(x-1\right)^3=8\)
\(\Leftrightarrow\left(x-1\right)^3=2^3\)
\(\Leftrightarrow x-1=2\)
\(\Leftrightarrow x=2+1\)
\(\Leftrightarrow x=3\)
Bài 4:
\(A=100+98+96+...+2-97-95-...-1\)
\(\Leftrightarrow A=\left(100+98+96+...+2\right)-\left(97+95+...+1\right)\)
\(\Leftrightarrow A=\left[\left(100+2\right).50:2\right]-\left[\left(97+1\right).49:2\right]\)
\(\Leftrightarrow A=2550-2401\)
\(\Leftrightarrow A=149\)
