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\(3^{x+1}+3^x=108\)
\(\Rightarrow3^x\left(1+3\right)=108\)
\(\Rightarrow3^x.4=108\)
\(\Rightarrow3^x=108:4\)
\(\Rightarrow3^x=27\)
\(27=3^3\)
\(3^x=3^3\)
\(\Rightarrow x=3\)
Vậy x = 3
3\(^{x+1}\)+ 3\(^x\)=108
3\(^x\).3 + 3\(^x\)= 108
3\(^x\)( 3 + 1 ) = 108
3\(^x\). 4 = 108
3\(^x\)= 27 = 3\(^3\)
x = 3
4,
a,\(\dfrac{x-1}{9}\)=\(\dfrac{8}{3}\)
[x- 1].3=9.8
[x- 1].3=72
x-1=72:3
x-1=24
x=24+1
x=25
e) \(\frac{-84}{14}< 3x< \frac{108}{9}\)
\(\Rightarrow-2< x< 4\)
Vậy \(-2< x< 4\)
d) \(\frac{x-3}{y-3}=\frac{4}{3}\)
Ta có: x=y+5
\(\Rightarrow\frac{y+5-3}{y-3}=\frac{4}{3}\)
\(\Rightarrow\frac{y+2}{y-3}=\frac{4}{3}\)
\(\Rightarrow\left(y+2\right).3=\left(y-3\right).4\)
\(3y+6=4y-12\)
\(6+12=4y-3y\)
\(y=18\)
\(\Rightarrow x=5+y=5+18=23\)
KL:............................
a) \(\frac{x-1}{9}=\frac{8}{3}\)
\(\Rightarrow\)\(\left(x-1\right).3=9.8\)
\(3x-3=72\)
\(3x=75\)
\(x=\frac{75}{3}\)
\(x=25\)
Câu b tương tự
\(\frac{x}{4}=\frac{18}{x+1}\)
\(\Rightarrow x.\left(x+1\right)=4.18\)
\(x.\left(x+1\right)=72\)
\(x.\left(x+1\right)=8.9\)
\(\Rightarrow x=8\)
1)
\(\frac{7.8^3-5.2^{10}}{\left(-16\right)^2}\)
= \(\frac{7.2^8.2-5.2^8.2^2}{16^2}\)
= \(\frac{2^8.\left(2.7-5.2^2\right)}{2^8}\)
= \(\frac{2^8.\left(-6\right)}{2^8}\)
= \(-6\)
\(\left(x-5\right)-27=18\)
\(x-5=45\)
\(x=50\)
vậy \(x=50\)
b) \(\left(3x-2^3\right).25=250\)
\(3x-8=10\)
\(3x=18\)
\(x=6\)
vậy \(x=6\)
c) \(108⋮x\)\(\Rightarrow x\inƯ\left(108\right)\) \(\Rightarrow x\in\left\{1;2;4;...;108\right\}\)
những ý sau làm tương tự
a)(x-5)-27=18
x-5=45
x=50
b)\(\left(3x-2^3\right).25=250\)
\(3x-2^3=10\)
\(3x=18\)
\(x=6\)
\(\Leftrightarrow\)\(x-\left(\frac{13x}{18}-\frac{4}{18}\right)=\frac{4}{9}\)
\(\Leftrightarrow\)\(\frac{18x}{18}-\frac{13x}{18}+\frac{4}{18}=\frac{4}{9}\)
\(\Leftrightarrow\)\(\frac{5x}{18}=\frac{4}{9}-\frac{4}{18}\)
\(\Leftrightarrow\)\(\frac{5x}{18}=\frac{2}{9}\)
\(\Leftrightarrow\)\(5x=\frac{18.2}{9}\)
\(\Leftrightarrow\)\(5x=4\)
\(\Leftrightarrow\)\(x=\frac{4}{5}\)
\(3^{x+1}+3^x=108\)
\(3^x\cdot3+3^x=108\)
\(3^x\cdot\left(3+1\right)=108\)
\(3^x=27=3^3\)
\(\Rightarrow x=3\)
\(3^{x+1}+3^x=108\)
(=)\(3^x.3+3^x=108\)
(=)\(3^x.\left(3+1\right)=108\)
(=)\(3^x.4=108\)
(=)\(3^x=27\)
(=)\(3^x=3^3\)
=>x=3