\(3^{x+3}-18.3^x=3^7\)

\(3^x.\left(3^3-18\right)=3^7\)

\(3^x.\left(27-18\right)=3^7\)

\(3^x.9=3^7\)

\(3^x.3^2=3^7\)

\(3^{x+2}=3^7\)

\(x+2=7\)

\(x=7-2\)

\(x=5\)

a: =5-78*32

=5-2496

=-2491

b: \(=6\left(9-6\right)=6\cdot3=18\)

c: \(=46\cdot\dfrac{\left(123-42\right)}{81}=46\)

d: \(=181+3-84+8\cdot25\)

=100+200

=300

e: \(=64\cdot35+140\cdot84-1=2240-1+11760\)

=14000-1

=13999

f: \(=3^3+25\cdot8-1=26+200=226\)

g: \(=3+2^4+1=16+4=20\)

h: \(=36:4\cdot3+2\cdot25-1=27+50-1=27+49=76\)

`36^{4}.16^{2}`

`=6^{8}.2^{8}`

`=(6.2)^8`

`=12^8`

`4^{6}.27^{4}`

`=2^{12}.3^{12}`

`=(2.3)^12`

`=6^12`

2 câu này không rõ đề

\(36^4\cdot16^2=1296^2\cdot16^2=429981696\)

\(4^6\cdot27^4=2^{12}\cdot3^{12}=2176782336\)

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 ....

1. 2^x=16\(\Rightarrow\)X=4

2. 2^2x-1=2⁷

\(\Rightarrow\)2⁷=2^2.4-1

Vậy x =4

x=4 nha chị

Ta đặt : \(A=1^2+2^2+3^2+...+12^2=625\)

\(\Rightarrow2A=2^2+4^2+6^2+...+24^2\)

\(\Leftrightarrow2A=1250\)

Vì \(1^2+2^2+3^2+......+12^2=625\)

\(\Rightarrow2^2+4^2+6^2+.......+24^2\)

\(=\left(1.2\right)^2+\left(2.2\right)^2+\left(3.2\right)^2+........+\left(12.2\right)^2\)

\(=1^2.2^2+2^2.2^2+3^2.2^2+.....+12^2.2^2\)

\(=1^2.4+2^2.4+3^2.4+......+12^2.4\)

\(=4.\left(1^2+2^2+3^2+.......+12^2\right)\)

\(=4.625=2500\)

2² + 4² + 6² + ... + 24²

= ( 2.1 )² + ( 2.2 )² + ( 2.3 )² + ... + ( 2.12 )² 

= 2².1² + 2².2² + 2².3² + ... + 2².12²

= 2²( 1² + 2² + 3² + ... + 12² )

= 4.625 = 2500

\(3^{x+1}+3^{x+2}=324\\ \Rightarrow3^{x+1}\left(1+3\right)=324\\ \Rightarrow3^{x+1}=324:4=81=3^4\\ \Rightarrow x+1=4\Rightarrow x=3\)