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a) (2n - 1)7 = 510 : 53
=> (2n - 1)7 = 57
=> 2n - 1 = 5
=> 2n = 6
=> n = 6 : 2
=> n = 3
b) 5n + 2 . 53 = 254
5n + 2 . 53 = (52)4
=> 5n + 2 + 3 = 52.4
=> 5n + 5 = 58
=> n + 5 = 8
=> n = 8 - 5
=> n = 3
c) 9n + 1 . 3n + 2 = 319
=> (32)(n + 1) . 3n + 2 = 319
=> 32(n + 1) . 3n + 2 = 319
=> 32(n + 1) + n + 2 = 319
=> 2(n + 1) + n + 2 = 19
=> 2n + 2 + n + 2 = 19
=> 3n + 4 = 19
=> 3n = 15
=> n = 5
d) 25n + 2 : 5n + 1 = 1255
=> (52)(n + 2) : 5n + 1 = (53)5
=> 52.(n + 2) : 5n + 1 = 53 . 5
=> 52.(n + 2) - (n + 1) = 515
=> 2(n + 2) - (n + 1) = 15
=> 2n + 4 - n - 1 = 15
=> n + 3 = 15
=> n = 12
a. (2n - 1)7 = 510 : 53
<=> (2n - 1)7 = 57
<=> 2n - 1 = 5
<=> n = 3
b. 5n+2 . 53 = 254
<=> 5n.52 . 53 = (52)4
<=> 5n = 53
<=> n = 3
c. 9n+1 . 3n+2 = 319
<=> 9n.9 . 3n.32 = 319
<=> 32n.32 . 3n.32 = 319
<=> 33n = 315
<=> 3n = 15
<=> n = 5
Câu d và e hơi mâu thuẫn
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CÂU 1
\(5^{n+1}+5^n=750\)
\(=>5^n\cdot5+5^n=750\)
\(=>5^n\cdot\left(5+1\right)=750\)
\(=>5^n\cdot6=750\)
\(=>5^n=750:6\)
\(=>5^n=125\)
\(=>5^n=5^3\)
\(=>n=3\)
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\(\left(125^{100}.2^{160}\right):\left(5^{289}.4^{80}\right)\)\(=\frac{\left(5^3\right)^{100}.2^{100}}{5^{289}.\left(2^2\right)^{80}}\)\(=\frac{5^{300}.2^{100}}{5^{289}.2^{160}}\)\(=\frac{5^{11}}{2^{60}}\)
\(\left(9^8.5^8\right):\left(3^7.27^3.5^4\right)\)\(=\frac{\left(3^2\right)^8.5^8}{3^7.\left(3^3\right)^3.5^4}=\frac{3^{16}.5^4}{3^7.3^9}=\frac{3^{16}.5^4}{3^{16}}=5^4=625\)
\(\left(1024.27^8\right):\left(2^9.3^{23}\right)=\frac{2^{10}.\left(3^3\right)^8}{2^9.3^{23}}=\frac{2.3^{24}}{3^{23}}=2.3=6\)
\(\left(625.2^7+25^2.64\right):\left(2^6.5^4.3\right)=\frac{25^2.128+25^2.64}{2^6.\left(5^2\right)^2.3}=\frac{25^2.\left(128+64\right)}{64.25^2.3}=\frac{192}{192}=1\)
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a)35-(12-(-14+(-2)))
=35-(12-(-12))
=35-(12+12)
=35-24
=11
b)49-(-54)-23
=49+54-23
=103-23
=80
c)5871:(928-((-82)+247))×5)
=5871:(928-165×5)
=5871:(928-825)
=5871:103
=57
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a)\(12:\left\{400:\left[500-\left(125+25×7\right)\right]\right\}\)
\(12:\left\{400:\left[500-300\right]\right\}\)
\(12:2\)
\(6\)
b)\(\left[\left(7-3^3:3^2\right):2^2+99\right]-100\)
\(=\left[4:4+99\right]-100\)
\(=100-100\)
\(=0\)
\(c,3^2×\left[\left(5^2-3\right):11\right]-2^4+2×10^3\)
\(=9×2-16+2×10000\)
\(=18-16+20000\)
\(=20002\)
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