a) 2^3x+2 = 4^x+5 = (2²)^x+5 = 2^2x+10

=> 3x + 2 = 2x + 10

=> 3x - 2x = 10 - 2

x = 8

b) 3^-1.3^x + 9.3^x = 28

3^x. ( 3^-1 + 9) = 28

3^x. 28/3 = 28

3^x = 3 = 3¹

=> x = 1

     \(2^{3x+2}=4^{x+5}\)

\(\Rightarrow2^{3x+2}=\left(2^2\right)^{x+5}\)

\(\Rightarrow3x+2=2\left(x+5\right)\)

\(\Rightarrow3x+2=2x+10\)

\(\Rightarrow3x-2x=10-2\Rightarrow x=8\)

      \(3^{-1}.3^x+9.3^x=28\)

\(\Rightarrow\frac{1}{3}.3^x+9.3^x=28\)

\(\Rightarrow3^x.\left(9+\frac{1}{3}\right)=28\)

\(\Rightarrow3^x.\frac{28}{3}=28\)

\(\Rightarrow3^x=3\Rightarrow x=1\)

Chúc bạn học tốt.

2ⁿ.(1/2+4)=9.32

2ⁿ*4,5=288

2ⁿ=64=2⁶

=> n=6

\(2^{-1}.2^n+4.2^n=9.2^5\)

\(2^n.2=9.2^5\)

\(\Rightarrow2^n=9.2^4\)

Ko có n nhé bn

2)adtccdtsbn và a-b=5 ta có

a/3=b/4=(a-b)/(3-4)=5/-1=-5

tự làm nốt a/3=-5 =>a=-15

Do \(\frac{3x-y}{x+y}=\frac{3}{4}\Rightarrow12x-4y=3x+3y\)

\(\Rightarrow12x-3x=3x+4y\Leftrightarrow9x=7y\Rightarrow\frac{x}{7}=\frac{y}{9}\)

Theo t/c dãy tỉ số bằng nhau

\(\Rightarrow\frac{x}{7}=\frac{y}{9}=\frac{x-2y}{7-2.9}=\frac{17}{-11}\)

=> x ; y

\(2;\frac{a}{3}=\frac{b}{4}=\frac{a-b}{3-4}=\frac{5}{-1}=-5\Rightarrow a=-15;b=-20\)

ADTCDTSBN

có: \(\frac{x}{2}=\frac{y}{5}=\frac{z}{15}=\frac{x+y+z}{2+5+15}=\frac{230}{22}=\frac{115}{11}.\)

=> x/2 = 115/11 => x  = 230/11

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bn tự lm típ nha!!!

Cách 2:

ta có: \(\frac{x}{2}=\frac{y}{5}=\frac{z}{15}=k\Rightarrow\hept{\begin{cases}x=2k\\y=5k\\z=15k\end{cases}}\)

mà x + y + z = 230

=> 2k + 5k + 15k = 230

k.(2+5+15) = 230

k.22 = 230

k = 115/11

=> x = 2k = 2. 115/11 = 230/11

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