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a) (5x - 12 ) : 4 = 318 : 315
( 5x - 12 ) : 4 = 33
( 5x - 12 ) : 4 = 27
5x - 12 = 108
5x = 120
x = 24
b) 5x3 - 102 = 35
5x3 - 100 = 35
5x3 = 135
x3 = 27
x3 = 33
=> x = 3
c) 65 - 4x+2 = 20180
65 - 4x+2 = 1
4x+2 = 64
4x+2 = 43
x + 2 = 3
=> x = 1
d) 2x+1 - 2x = 32
2x . ( 2 - 1 ) = 32
2x . 1 = 32
2x = 32
2x = 25
=> x = 5
\(A=\frac{72^3\times54^2}{108^4}\)
\(\Rightarrow A=\frac{\left(2^3\times3^2\right)^3\times54^2}{\left(54\times2\right)^4}\)
\(\Rightarrow A=\frac{\left(2^3\right)^3\times\left(3^2\right)^3\times54^2}{54^4\times2^4}\)
\(\Rightarrow A=\frac{2^9\times3^6\times54^2}{54^2\times54^2\times2^4}\)
\(\Rightarrow A=\frac{2^5\times3^6}{54^2}\)
\(\Rightarrow A=\frac{2^5\times3^6}{\left(2\times3^3\right)^2}\)
\(\Rightarrow A=\frac{2^2\times2^3\times3^6}{2^2\times\left(3^3\right)^2}\)
\(\Rightarrow A=\frac{2^3\times3^6}{3^6}\)
\(\Rightarrow A=2^3=8\)
\(B=\frac{3^{10}\times11+3^{10}\times5}{3^9\times2^4}\)
\(\Rightarrow B=\frac{3^{10}\times\left(11+5\right)}{3^9\times2^4}\)
\(\Rightarrow B=\frac{3^{10}\times16}{3^9\times16}\)
\(\Rightarrow B=\frac{3^{10}}{3^9}=3\)
\(\frac{72^3.54^2}{108^4}=\frac{\left(2^3.3^2\right)^3.\left(2.3^3\right)^2}{\left(2^2.3^3\right)^4}=\frac{\left(2^3\right)^3.\left(3^2\right)^3.2^2.\left(3^3\right)^2}{\left(2^2\right)^4.\left(3^3\right)^4}=\frac{2^9.3^6.2^2.3^6}{2^8.3^{12}}=\frac{\left(2^9.2^2\right)\left(3^6.3^6\right)}{2^8.3^{12}}=\frac{2^{9+2}.3^{6+6}}{2^8.3^{12}}=\frac{2^{11}.3^{12}}{2^8.3^{12}}=\frac{2^3.2^8.3^{12}}{2^8.3^{12}}=2^3=8\)
\(\left(72.10^3+18.10^3\right)-\left(5x+3.10^3\right)=2.10^3\)
\(10^3.\left(72+18\right)-5x-3.10^3=2.10^3\)
\(10^3.90-5x-3000=2000\)
\(10^3.90-5x=5000\)
\(90000-5x=5000\)
\(5x=85000\)
\(x=17000\)