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3x+2+3x+3=108
3x . 32 + 3x . 33 = 108
3x . ( 32 + 33 ) = 108
3x . 36 =108
3x = 108 : 36
3x = 3
3x = 31
=> x = 1
\(125=5^3\)
\(25^2=\left(5^2\right)^2=5^{2.2}=5^4\)
\(\left(5^3\right)^2=5^{3.2}=5^6\)
\(125^5=\left(5^3\right)^5=5^{3.5}=5^{15}\)
\(625^4=\left(5^4\right)^4=5^{4.4}=5^{16}\)
\(125.5^2=5^3.5^2=5^{3+2}=5^5\)
125 = 53
252 = (52)2 = 54
(53)2 = 56
1255 = ( 53)5 = 515
6254 = (54)4 = 516
125 . 52 = 53 . 52 = 55
a) \(\left(20.2^4+12.2^4-48.2^2\right):8^2\)
\(=\left(20.2^4+12.2^4-12.2^4\right):8^2\)
\(=2^4.\left(20+12-12\right):8^2\)
\(=16.20:64\)
\(=5\)
=54 . (75+175) ÷ 15625
=54 . .250 ÷ 56
=(54 ÷56) . 250
=0,04 . 250
=10
A = (75.54 + 175.54 ) : ( 20 . 25 . 125 - 625 . 75 )
= [(75 + 175).54 ] : (20.25.25.5 - 625.75)
= (250.54 ) : [ 625.(100 - 75)]
= (250.54 ) : (54 . 25)
= 250 : 25
= 10
\(\Rightarrow\left(5^2\right)^{4x+2}.\left(5^3\right)^{2x+4}=\left(5^4\right)^4\)
\(\Rightarrow5^{8x+4}.5^{6x+12}=5^{16}\)
\(\Rightarrow5^{8x}.5^4.5^{6x}.5^{12}=5^{16}\)
\(\Rightarrow5^{14x}.5^{16}=5^{16}\)
\(\Rightarrow5^{14x}=1\)
\(\Rightarrow14x=0\)
=> x=0