64 . 4^x = 168

<=> 43. 4^x = 416

=> 3 + x = 16

<=> x = 13

Vậy x = 13

2^x.16² = 1024

<=> 2^x. 2⁸ = 210

=> x + 8 = 10

<=> x = 2

Vậy x = 2

b: Ta có: \(2^x\cdot16^2=1024\)

\(\Leftrightarrow2^x\cdot2^8=2^{10}\)

\(\Leftrightarrow x+8=10\)

hay x=2

  64.4^x=16³

  2⁶. (2²)^x = (2⁴)³

=> 2⁶. 2^2x = 2¹²

        2^2x   = 2 ¹² : 2⁶

       2^2x   = 2⁶

  =>  2x = 6

         x = 6 :2

         x=3

- Vậy x =3

1) \(2^x=4^3 \Leftrightarrow2^x=2^6\Leftrightarrow x=6\)

2) \(2^x=4^6\Leftrightarrow2^x=2^{12}\Leftrightarrow x=12\)

3) \(3^x=9^{10}\Leftrightarrow3^x=3^{20}\Leftrightarrow x=20\)

1) 2�=43⇔2�=26⇔�=62x=43⇔2x=26⇔x=6

2) 2�=46⇔2�=212⇔�=122x=46⇔2x=212⇔x=12

3) 3�=910⇔3�=320⇔�=203x=910⇔3x=320⇔x=20

1) 2�=43⇔2�=26⇔�=62x=43⇔2x=26⇔x=6

2) 2�=46⇔2�=212⇔�=122x=46⇔2x=212⇔x=12

3) 3�=910⇔3�=320⇔�=203x=910⇔3x=320⇔x=20

đoạn kia là \(4^{x-2}\)hay là \(4^x-2\)z

\(A=3+3^2+....+3^{99}\)

\(3A=3^2+3^3+...+3^{100}\)

\(3A-A=3^2+3^3+...+3^{100}-3-3^2-...-3^{99}\)

\(2A=3^{100}-3\)

\(A=\dfrac{3^{100}-3}{2}\)

\(\Rightarrow2A+3=9^{2x+6}\)

\(\Rightarrow2\cdot\dfrac{3^{100}-3}{2}+3=\left(3^2\right)^{2x+6}\)

\(\Rightarrow3^{100}-3+3=3^{2\left(2x+6\right)}\)

\(\Rightarrow3^{100}=3^{4x+12}\)

\(\Rightarrow4x+12=100\)

\(\Rightarrow4x=88\)

\(\Rightarrow x=22\)

Câu a mình ko bt trình bày thông cảm

b) \(^{2^x.\left(2^2\right)^2=\left(2^3\right)^2}\)

\(2^x.2^4=2^6\)

\(2^x=2^6:2^4\)

\(2^x=2^2\)

\(x=2\)

a)(x^5)^10=x<=>x=0 hoặc 1

các bạn ơi cho minh hoi cai:

10 mũ x+4y=2013 

Hãy cho minh dap an chinh xac 

Cam on cac ban da xem bai viet cua minh 

và mình cũng cảm ơn những ai đã trả lời cho minh va hay cho minh nhe!

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) \(25^{2n}:5^n=125^2\Rightarrow\left(5^2\right)^{2n}:5^n=\left(5^3\right)^2\Rightarrow5^{4n}:5^n=5^6\Rightarrow\Rightarrow5^{3n}=5^6\Rightarrow3n=6\Rightarrow n=3\)

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) \(\dfrac{3}{2.4^x}+\dfrac{5}{3.4^{x+2}}=\dfrac{3}{2.4^8}+\dfrac{5}{3.4^{10}}\)

\(\Rightarrow\dfrac{3}{2.4^x}-\dfrac{3}{2.4^8}+\dfrac{5}{3.4^{x+2}}-\dfrac{5}{3.4^{10}}=0\)

\(\Rightarrow\dfrac{3}{2}\left(\dfrac{1}{4^x}-\dfrac{1}{4^8}\right)+\dfrac{5}{3.4^2}\left(\dfrac{1}{4^x}-\dfrac{1}{4^8}\right)=0\)

\(\Rightarrow\left(\dfrac{1}{4^x}-\dfrac{1}{4^8}\right)\left(\dfrac{3}{2}+\dfrac{5}{3.4^2}\right)=0\)

\(\Rightarrow\dfrac{1}{4^x}-\dfrac{1}{4^8}=0\)

\(\Rightarrow\dfrac{4^8-4^x}{4^{x+8}}=0\Rightarrow4^8-4^x=0\left(4^{x+8}>0\right)\Rightarrow4^x=4^8\Rightarrow x=8\)

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