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27 tháng 7 2023
Bài 6 :
a) \(\dfrac{625}{5^n}=5\Rightarrow\dfrac{5^4}{5^n}=5\Rightarrow5^{4-n}=5^1\Rightarrow4-n=1\Rightarrow n=3\)
b) \(\dfrac{\left(-3\right)^n}{27}=-9\Rightarrow\dfrac{\left(-3\right)^n}{\left(-3\right)^3}=\left(-3\right)^2\Rightarrow\left(-3\right)^{n-3}=\left(-3\right)^2\Rightarrow n-3=2\Rightarrow n=5\)
c) \(3^n.2^n=36\Rightarrow\left(2.3\right)^n=6^2\Rightarrow\left(6\right)^n=6^2\Rightarrow n=6\)
d) \(25^{2n}:5^n=125^2\Rightarrow\left(5^2\right)^{2n}:5^n=\left(5^3\right)^2\Rightarrow5^{4n}:5^n=5^6\Rightarrow\Rightarrow5^{3n}=5^6\Rightarrow3n=6\Rightarrow n=3\)
27 tháng 7 2023
Bài 7 :
a) \(3^x+3^{x+2}=9^{17}+27^{12}\)
\(\Rightarrow3^x\left(1+3^2\right)=\left(3^2\right)^{17}+\left(3^3\right)^{12}\)
\(\Rightarrow10.3^x=3^{34}+3^{36}\)
\(\Rightarrow10.3^x=3^{34}\left(1+3^2\right)=10.3^{34}\)
\(\Rightarrow3^x=3^{34}\Rightarrow x=34\)
b) \(5^{x+1}-5^x=100.25^{29}\Rightarrow5^x\left(5-1\right)=4.5^2.\left(5^2\right)^{29}\)
\(\Rightarrow4.5^x=4.25^{2.29+2}=4.5^{60}\)
\(\Rightarrow5^x=5^{60}\Rightarrow x=60\)
c) Bài C bạn xem lại đề
d) \(\dfrac{3}{2.4^x}+\dfrac{5}{3.4^{x+2}}=\dfrac{3}{2.4^8}+\dfrac{5}{3.4^{10}}\)
\(\Rightarrow\dfrac{3}{2.4^x}-\dfrac{3}{2.4^8}+\dfrac{5}{3.4^{x+2}}-\dfrac{5}{3.4^{10}}=0\)
\(\Rightarrow\dfrac{3}{2}\left(\dfrac{1}{4^x}-\dfrac{1}{4^8}\right)+\dfrac{5}{3.4^2}\left(\dfrac{1}{4^x}-\dfrac{1}{4^8}\right)=0\)
\(\Rightarrow\left(\dfrac{1}{4^x}-\dfrac{1}{4^8}\right)\left(\dfrac{3}{2}+\dfrac{5}{3.4^2}\right)=0\)
\(\Rightarrow\dfrac{1}{4^x}-\dfrac{1}{4^8}=0\)
\(\Rightarrow\dfrac{4^8-4^x}{4^{x+8}}=0\Rightarrow4^8-4^x=0\left(4^{x+8}>0\right)\Rightarrow4^x=4^8\Rightarrow x=8\)
VM
13 tháng 8 2019
3.
a) \(\left(x-1\right)^3=125\)
=> \(\left(x-1\right)^3=5^3\)
=> \(x-1=5\)
=> \(x=5+1\)
=> \(x=6\)
Vậy \(x=6.\)
b) \(2^{x+2}-2^x=96\)
=> \(2^x.\left(2^2-1\right)=96\)
=> \(2^x.3=96\)
=> \(2^x=96:3\)
=> \(2^x=32\)
=> \(2^x=2^5\)
=> \(x=5\)
Vậy \(x=5.\)
c) \(\left(2x+1\right)^3=343\)
=> \(\left(2x+1\right)^3=7^3\)
=> \(2x+1=7\)
=> \(2x=7-1\)
=> \(2x=6\)
=> \(x=6:2\)
=> \(x=3\)
Vậy \(x=3.\)
Chúc bạn học tốt!
NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
23 tháng 7 2023
a, (-0,2)2 \(\times\) 5 - \(\dfrac{2^{13}\times27^3}{4^6\times9^5}\)
= 0,04 \(\times\) 5 - \(\dfrac{2^{13}\times3^9}{2^{12}\times3^{10}}\)
= 0,2 - \(\dfrac{2}{3}\)
= \(\dfrac{2}{10}\) - \(\dfrac{2}{3}\)
= - \(\dfrac{7}{15}\)
b, \(\dfrac{5^6+2^2.25^3+2^3.125^2}{26.5^6}\)
= \(\dfrac{5^6+4.5^6+8.5^6}{26.5^6}\)
= \(\dfrac{5^6.\left(1+4+8\right)}{26.5^6}\)
= \(\dfrac{1}{2}\)
TD
Trần Đức Phát
VIP
23 tháng 7 2023
a, (-0,2)2 ×× 5 - 213×27346×9546×95213×273
= 0,04 ×× 5 - 213×39212×310212×310213×39
= 0,2 - 2332
= 210102 - 2332
= - 715157
b, 56+22.253+23.125226.5626.5656+22.253+23.1252
= 56+4.56+8.5626.5626.5656+4.56+8.56
= 56.(1+4+8)26.5626.5656.(1+4+8)
= 1221
CK
2
T
11 tháng 8 2023
Có: \(\left(\dfrac{2}{5}\right)^{13.x}=\left(\dfrac{8}{125}\right)^5\)
\(\Rightarrow\left(\dfrac{2}{5}\right)^{13.x}=\left[\left(\dfrac{2}{5}\right)^3\right]^5\)
\(\Rightarrow\left(\dfrac{2}{5}\right)^{13.x}=\left(\dfrac{2}{5}\right)^{15}\)
\(\Rightarrow13.x=15\)
\(\Rightarrow x=\dfrac{15}{13}\)
7 tháng 9 2016
\(a,\frac{8^{12}.5^{21}}{2^{17}.10^{19}}=\frac{\left(2^3\right)^{12}.5^{21}}{2^{17}.2^{19}.5^{19}}=\frac{2^{36}.5^{21}}{2^{36}.5^{19}}=25\)
\(b,\left(x-5\right).\left(x+\frac{1}{2}\right)=0\)
\(\Rightarrow x-5=0\)hoặc \(x+\frac{1}{2}=0\)
\(x=5\)hoặc \(x=-\frac{1}{2}\)
\(c,\left|x-6\right|-\frac{1}{2}=\frac{3}{2}\)
\(\left|x-6\right|=2\)
\(\Rightarrow x-6=2\)hoặc \(x-6=-2\)
\(x=8\)hoặc \(x=4\)
23 tháng 7 2023
a) 4.25-12.5+170:10
=100-60+17
=40+17
=57
b) (7+33:32).4-3
=(7+3).4-3
=10.4-3
=40-3
=37
c) 12:{400:[500-(125+25.7)]}
=12:{400:[500-(125+175)]}
=12:{400:[500-300]}
=12:{400:200}
=12:2
=6
d) 168+{[2.(24+32)-2560]:72}
=168+{[2.(16+9)-1]:49}
=168+{[2.25-1]:49}
=168+{[50-1]:49}
=168+{49:49}
=168+1
=169
29 tháng 6 2018
a) Ta có: \(\left(\frac{1}{2}\right)^m=\frac{1}{32}\)
Mà \(\frac{1}{32}=\left(\frac{1}{2}\right)^5\)
\(\Rightarrow\left(\frac{1}{2}\right)^m=\left(\frac{1}{2}\right)^5\Rightarrow m=5\)
b)Ta có: \(\frac{343}{125}=\left(\frac{7}{5}\right)^3\)
Mà \(\left(\frac{7}{5}\right)^3=\left(\frac{7}{5}\right)^n\Rightarrow n=3\)
29 tháng 6 2018
\(a)\) \(\left(\frac{1}{2}\right)^m=\frac{1}{32}\)
\(\Leftrightarrow\)\(\left(\frac{1}{2}\right)^m=\frac{1^5}{2^5}\)
\(\Leftrightarrow\)\(\left(\frac{1}{2}\right)^m=\left(\frac{1}{2}\right)^5\)
\(\Leftrightarrow\)\(m=5\)
Vậy \(m=5\)
\(b)\) \(\frac{343}{125}=\left(\frac{7}{5}\right)^n\)
\(\Leftrightarrow\)\(\frac{7^3}{5^3}=\left(\frac{7}{5}\right)^n\)
\(\Leftrightarrow\)\(\left(\frac{7}{5}\right)^3=\left(\frac{7}{5}\right)^n\)
\(\Leftrightarrow\)\(n=3\)
Vậy \(n=3\)
Chúc bạn học tốt ~
N
11 tháng 9 2020
a) \(\frac{75^3.3^7}{81^4.5^6}=\frac{5^3.3^3.5^3.3^7}{\left(3^4\right)^4.5^6}=\frac{5^6.3^3.3^7}{3^{16}.5^6}=\frac{3^{10}}{3^{16}}=\frac{1}{3^6}=\frac{1}{729}\)
b) \(\frac{6^6.4^2}{3^{12}.2^8}=\frac{2^6.3^6.\left(2^2\right)^2}{3^{12}.2^8}=\frac{2^6.3^6.2^4}{3^{12}.2^8}=\frac{2^{10}.3^6}{3^{12}.2^8}=\frac{2^2.1}{3^6}=\frac{4}{729}\)
c) \(\frac{34^5.2^5}{2^{14}.17^5}=\frac{2^5.17^5.2^5}{2^{14}.17^5}=\frac{2^{10}}{2^{14}}=\frac{1}{2^4}=\frac{1}{16}\)