Bài 1:

2^\(x\) = 4

2\(^x\) = 2²

 \(x=2\)

Vậy \(x=2\)

Bài 2:

2\(^x\) = 8

2\(^x\) = 2³

\(x=3\)

Vậy \(x=3\)

Bài 3

2\(^x\) = 16

2\(^x\) = 2⁴

  \(x=4\)

Vậy \(x=4\)

a) x=3

b) x=1

c) x=1 hoặc -5

d) x=2

e) x=2

g) x=2

h) x=1 hoặc x=0 hoặc x=-1

i) x=-1 hoặc x=0

\(a.4^x=64\)

\(4^x=4^3\)

\(\Rightarrow x=3\)

\(b,3^{x\times4}=81\)

\(3^{x\times4}=3^4\)

\(x\times4=4\)

\(\Rightarrow x=1\)

\(c,\left(2+x\right)^4=81\)

     \(\left(2+x\right)^4=3^4\) 

       \(2+x=3\)

                \(x=3-2\)

                \(x=1\)

\(d,5^{x\times5}=125\)

     \(5^{x\times5}=5^3\)

        \(x\times5=3\)

        \(x=3:5\)

        \(x=\frac{3}{5}\)

a=197

b=157

c=121

d=16400

a)197

b)157

c)121

d)16400

a, 204-84:12                                                                   b,5⁶:5³+2³.2²

=204-7                                                                                 =5³+2⁵

=197                                                                                     =125+32

                                                                                              =157

c,15.2³+4.3²-5.7                                                               d,164.53+47.164

=15.4²+4.3²-35                                                                    =164(53+47)

=4.(60+9)-35                                                                        =164.100

=4.69-35                                                                               =16400

=276-35

=341

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

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

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

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

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

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

5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha

1) \(2^x-15=17\)

\(\Leftrightarrow2^x=32=2^5\)

\(\Rightarrow x=5\)

2) \(\left(7x-11\right)^3=25\cdot5^2+200\)

\(\Leftrightarrow\left(7x-11\right)^3=825\)

\(\Leftrightarrow7x-11=\sqrt[3]{825}\)

\(\Leftrightarrow7x=11+\sqrt[3]{825}\)

\(\Rightarrow x=\frac{11+\sqrt[3]{825}}{7}\)

3) \(\left(x+1\right)^{100}-3\left(x+1\right)^{99}=0\)

\(\Leftrightarrow\left(x+1\right)^{99}\left(x-2\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}\left(x+1\right)^{99}=0\\x-2=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=-1\\x=2\end{cases}}\)

4) \(4x+5\left(x+3\right)=105\)

\(\Leftrightarrow9x+15=105\)

\(\Leftrightarrow9x=90\)

\(\Rightarrow x=10\)

5) \(5\cdot\left(x-2\right)+10\left(x+3\right)=170\)

\(\Leftrightarrow5\left[x-2+2\left(x+3\right)\right]=170\)

\(\Leftrightarrow3x+4=34\)

\(\Leftrightarrow3x=30\)

\(\Rightarrow x=10\)

cảm ơn bạn nhá NGUYỄN MINH ĐĂNG

a, \(390-\left(x-7\right)=13^2:12\)

\(390-\left(x-7\right)=\) \(\dfrac{169}{12}\)

\(x-7=390-\dfrac{169}{12}\)

\(x-7=\dfrac{4511}{12}\)

\(x=\dfrac{4511}{12}+7\)

\(x=\dfrac{4595}{12}\)

Vậy ...

b, \(\left(x-35.2^2\right):7=3^3-24\)

\(\left(x-35.4\right):7=27-24\)

\(\left(x-140\right):7=3\)

\(\Leftrightarrow\left(x-140\right)=3.7\)

\(\Leftrightarrow x-140=21\)

\(\Leftrightarrow x=161\)

Vậy .....

c) \(x-6:2-\left(4^2.3-24\right):2:6=3\)

\(x-3-\left(16.3-24\right):2:6=3\)

\(x-3-\left(48-24\right):2:6=3\)

\(x-3-24:2:6=3\)

\(x-3-2=3\)

\(x=3+2+3\)

\(x=8\)

Vậy ......

d) \(4x-5=5+5^2+5^3+.....+5^{99}\)

Đặt :

\(A=5+5^2+.........+5^{99}\)

\(\Leftrightarrow5A=5^2+5^3+..........+5^{100}\)

\(\Leftrightarrow5A-A=\left(5^2+5^3+......+5^{100}\right)-\left(5+5^2+....+5^{99}\right)\)

\(\Leftrightarrow4A=5^{100}-5\)

\(\Leftrightarrow A=\dfrac{5^{100}-5}{4}\)

\(\Leftrightarrow4x+5=\dfrac{5^{100}-5}{4}\)

Đến đây thì sao nữa nhỉ ?

e) \(\left(2x-1\right)^4=625\)

\(\Leftrightarrow\left[{}\begin{matrix}\left(2x-1\right)^4=5\\\left(2x-1\right)^4=-5\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}2x-1=5\\2x-1=-5\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-2\end{matrix}\right.\)

Vậy ....