Tìm n:
\(3^{2n-1}+2.9^{n-1}=135\)
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30 tháng 9 2017
\(3^{2n-1}+2.9^{n-1}=135\)
\(\Leftrightarrow3^{2n-1}+2.\left(3^2\right)^{n-1}=135\)
\(\Leftrightarrow3^{2n-1}+2.3^{2n-2}=135\)
\(\Leftrightarrow3^{2n-1}+2.3^{2n-1}.\frac{1}{3}=135\)
\(\Leftrightarrow3^{2n-1}.\left(1+2.\frac{1}{3}\right)=135\)
\(\Leftrightarrow3^{2n-1}.\frac{5}{3}=135\)
\(\Leftrightarrow3^{2n-1}=135:\frac{5}{3}=81\)
\(\Leftrightarrow3^{2n-1}=3^4\Leftrightarrow2n-1=4\)
\(\Leftrightarrow2n=5\Rightarrow n=\frac{5}{2}\)
Vậy \(n=\frac{5}{2}\).
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24 tháng 4 2020
Câu 1:
a) Ta có: 2n+1 là số lẻ∀n
⇒\(\left(-1\right)^{2n+1}=-1\)
Ta có: \(\left(-25\right)\cdot21\cdot\left(-2\right)^2\cdot\left(-\left|-3\right|\right)\cdot\left(-1\right)^{2n+1}\)
\(=-25\cdot21\cdot4\cdot\left(-3\right)\cdot\left(-1\right)\)
\(=75\cdot84\cdot\left(-1\right)\)
\(=-6300\)
b) Ta có: \(\left(-5\right)^3\cdot67\cdot\left(-\left|-2^3\right|\right)\cdot\left(-1\right)^{2n}\)
\(=-125\cdot67\cdot\left(-8\right)\)
\(=1000\cdot67=67000\)
c) Ta có: \(35\cdot18-5\cdot7\cdot28\)
\(=35\cdot18-35\cdot28\)
\(=35\cdot\left(18-28\right)=35\cdot\left(-10\right)=-350\)
d) Ta có: \(24\cdot\left(16-5\right)-16\cdot\left(24-5\right)\)
\(=24\cdot16-24\cdot5-24\cdot16+16\cdot5\)
\(=-24\cdot5+16\cdot5\)
\(=5\cdot\left(-24+16\right)=5\cdot\left(-8\right)=-40\)
e) Ta có: \(29\cdot\left(19-13\right)-19\cdot\left(19-13\right)\)
\(=6\cdot\left(29-19\right)=6\cdot10=60\)
g)Sửa đề: \(31\cdot\left(-18\right)+31\cdot\left(-81\right)-31\)
Ta có: \(31\cdot\left(-18\right)+31\cdot\left(-81\right)-31\)
\(=31\cdot\left(-18-81-1\right)\)
\(=31\cdot\left(-100\right)=-3100\)
h) Ta có: \(\left(-12\right)\cdot47+\left(-12\right)\cdot52+\left(-12\right)\)
\(=-12\cdot\left(47+52+1\right)\)
\(=-12\cdot100=-1200\)
k) Ta có: \(13\cdot\left(23+22\right)-3\cdot\left(17+28\right)\)
\(=13\cdot45-3\cdot45\)
\(=45\cdot\left(13-3\right)=45\cdot10=450\)
m) Ta có: \(-48+48\cdot\left(-78\right)+48\cdot\left(-21\right)\)
\(=48\cdot\left(-1-78-21\right)\)
\(=48\cdot\left(-100\right)=-4800\)
n) Ta có: \(135\cdot\left(171-123\right)-171\cdot\left(135-123\right)\)
\(=135\cdot171-135\cdot123-171\cdot135+171\cdot123\)
\(=123\cdot\left(-135+171\right)=123\cdot36=4428\)
30 tháng 3 2020
jup đi mak
ai bt lm hộ cái zùi trả công cho!!!!!!!1
\(\Leftrightarrow9^n\cdot\dfrac{1}{3}+2\cdot9^n\cdot\dfrac{1}{9}=135\)
\(\Leftrightarrow9^n\cdot\dfrac{5}{9}=135\)
\(\Leftrightarrow9^n=243\)
\(\Leftrightarrow3^{2n}=243\)
=>2n=5
hay n=5/2