\(3^x+3^{x-2}=270\)

\(3^x+3^{x-2}=10\cdot3^3\)\(\Rightarrow\frac{3^x+3^{x-2}}{3}=3^{x-3}+3^{x-5}=10\)

\(3^{x-3}=\left(3^x\right)-3^3\)

\(\frac{3^x}{3^3}+\frac{3^x}{3^5}=10\)

\(\Rightarrow10\cdot3^{x-5}=2\cdot5\)

\(\Rightarrow3^{x-5}=1;x=5\)

\(3^{x+4}+3^{x+2}=270\)

\(< =>3^x.81+3^x.9=270\)

\(< =>3^x=\frac{270}{90}=3< =>x=1\)

\(3^{x+4}+3^{x+2}=270\)

\(\Leftrightarrow3^x.81+3^x.9=270\)

\(\Leftrightarrow3^x\left(81+9\right)=270\)

\(\Leftrightarrow3^x.90=270\)

\(\Leftrightarrow3^x=3\)

\(\Leftrightarrow x=1\)

3^{x + 4} + 3^{x + 2} = 270

3⁵ + 3³ = 270

= > x = 5 - 4 = 1

=> x = 3 - 2 = 1

=> x = 1

3^{x + 4} + 3^{x + 2} = 270

10.3^{x + 2} = 270

     3^{x + 2} = 270 : 10

     3^{x + 2} = 27

     3^{x + 2} = 3³

       x + 2 = 3

       x       = 3 - 2

       x       = 1

[(2x - 4) + 9]³ = 3⁶

(2x - 4 + 9)³ = 729

x = 2

125=5*3

729=3*6

\(125=x^3\)

\(\Leftrightarrow5^3=x^3\)

\(\Rightarrow x=5\)

Vậy x=5

\(729=x^6\)

\(\Rightarrow3^6=x^6\)

\(\Rightarrow x=3\)

Vậy x=3

\(x=-280\)
 

HD dùng PP Quy đồng tử (không quy đồng Mẫu)

\(\left(\frac{x+10}{270}+10\right)+\left(\frac{x+20}{260}+10\right)=\left(\frac{x+30}{250}+10\right)+\left(\frac{x+40}{240}+10\right)\\ \)

\(\left(x+280\right)\left(....\right)=0\)chú ý (...) thường khác không nếu bằng =0=> đúng với mọi x

nếu khác không=> x=-280

sai đề bài rồi bạn ơi

ko chép lại đầu bài nha                  

=(53x+800):7020=(49x+147):6000 

=(53x+800).6000=70

x=145,0369515 

lưu ý:mik làm theo cách suy luận nhé @@@

Kurima:

\(x^2=4\)          ;  \(125=5^x\)

\(x^2=2^2\)        ;  \(5^3=5^x\)

\(\Rightarrow x=2\)       ;  \(\Rightarrow x=3\)

:3, Chúc bạn học tốt!!!

A=7 B=1 OR =0 C=2 D=4.5.6

a: \(2^{x}\cdot4=128\)

=>\(2^{x}=\frac{128}{4}=32=2^5\)

=>x=5

b: \(x^{15}=x\)

=>\(x^{15}-x=0\)

=>\(x\left(x^{14}-1\right)=0\)

=>\(\left[\begin{array}{l}x=0\\ x^{14}-1=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=0\\ x^{14}=1\end{array}\right.\Rightarrow\left[\begin{array}{l}x=0\\ x=1\end{array}\right.\)

c: \(\left(2x+1\right)^3=125\)

=>\(\left(2x+1\right)^3=5^3\)

=>2x+1=5

=>2x=5-1=4

=>\(x=\frac42=2\)

d: \(\left(x-5\right)^4=\left(x-5\right)^6\)

=>\(\left(x-5\right)^6-\left(x-5\right)^4=0\)

=>\(\left(x-5\right)^4\cdot\left\lbrack\left(x-5\right)^2-1\right\rbrack=0\)

=>\(\left(x-5\right)^4\cdot\left(x-5-1\right)\left(x-5+1\right)=0\)

=>\(\left(x-5\right)^4\cdot\left(x-6\right)\left(x-4\right)=0\)

=>\(\left[\begin{array}{l}x-5=0\\ x-6=0\\ x-4=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=5\\ x=6\\ x=4\end{array}\right.\)

Bài 1:

6) 3x + 2³ = 17 + 3²

3x + 8 = 17 + 9

3x + 8 = 26

3x = 26 - 8

3x = 18

x = 18 : 3

x = 6

Vậy x = 6

Bài 2:

3) 145 - (125 + x) = 12

125 + x = 145 - 12

125 + x = 133

x = 133 - 125

x = 8

Vậy x = 8

6) 3³ - (x - 5) = 2²

27 - (x - 5) = 4

x - 5 = 27 - 4

x - 5 = 23

x = 23 + 5

x = 28

Vậy x = 28

9) (x + 7) - 15⁰ = 202 - 19

(x + 7) - 1 = 189

x + 7 = 189 + 1

x + 7 = 190

x = 190 - 7

x - 183

Vậy x = 183