a)7.2^x=56⇔2^x=8⇔2^x=2³⇔x=3

b)(2x+1)³=9.81⇔(2x+1)³=9³⇔2x+1=9⇔2x=8⇔x=4

c)x³=8²⇔x³=2⁶⇔x=2²⇔x=4

d)4.2^x-3=1⇔4.2^x=4⇔2^x=1⇔2^x=2⁰⇔x=0

e)2.3^x=162⇔3^x=81⇔3^x=3⁴⇔x=4

a) \(3\left(x-1\right)^2\cdot3x\left(x-5\right)=0\)

\(\Rightarrow9x\left(x-1\right)^2\left(x-5\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x=0\\x-1=0\\x-5=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\x=1\\x=5\end{matrix}\right.\)

b) \(\left(x+3\right)^2-5x-15=0\)

\(\Rightarrow\left(x+3\right)^2-5\left(x+3\right)=0\)

\(\Rightarrow\left(x+3\right)\left(x+3-5\right)=0\)

\(\Rightarrow\left(x+3\right)\left(x-2\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x+3=0\\x-2=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-3\\x=2\end{matrix}\right.\)

c) \(2x^5-4x^3+2x=0\)

\(\Rightarrow2x\left(x^4-2x^2+1\right)=0\)

\(\Rightarrow2x\left[\left(x^2\right)^2-2\cdot x^2\cdot1+1^2\right]=0\)

\(\Rightarrow2x\left(x^2-1\right)^2=0\)

\(\Rightarrow2x\left(x-1\right)^2\left(x+1\right)^2=0\)

\(\Rightarrow\left[{}\begin{matrix}x=0\\x-1=0\\x+1=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\x=1\\x=-1\end{matrix}\right.\)

\(\text{#}Toru\)

Câu này thiếu -1 trên tử rồi :v

Tham khảo câu trả lời của mod Lâm  Đọc bị lú rồi :D

`2^(x+2) . 3^(x+1) . 5^x = 10800`

`=> 2^x. 2^2. 3^x. 3. 5^x=10800`

`=> (2.3.5)^x. (4.3)=10800`

`=> 30^x. 12=10800`

`=> 30^x=10800:12`

`=> 30^x=900`

`=> 30^x=30^2`

`=> x=2`

\(2^{x+2}.3^{x+1}.5^x=10800\\ 2^x.2^2.3^x.3.5^x=10800\\30^x.12=10800\\ 30^x=10800:12\\ 30^x=900\\ 30^x=30^2\\ x=2\)

a: =>3[(2x-1)^2-4]=49*125:175+196=231

=>(2x-1)^2-4=77

=>(2x-1)^2=81

=>2x-1=9 hoặc 2x-1=-9

=>x=5 hoặc x=-4

b: \(\Leftrightarrow2\cdot3^x\cdot3-4^3=7^2\cdot\left(27-25\right)\)

=>\(6\cdot3^x=49\cdot2+64=162\)

=>3^x=27

=>x=3

Lời giải:
a.

$3[(2x-1)^2-4]-14^2=7^2.5^3:175=35$

$3[(2x-1)^2-4]=35+14^2=231$

$(2x-1)^2-4=231:3=77$

$(2x-1)^2=77+4=81=9^2=(-9)^2$

$\Rightarrow 2x-1=9$ hoặc $2x-1=-9$

$\Rightarrow x=5$ hoặc $x=-4$

b.

$2.3^{x+1}-4^{10}:4^7=(7^5:7^3).(3^3-5^2)=7^2.2=98$

$2.3^{x+1}-4^3=98$

$2.3^{x+1}=98+4^3=162$

$3^{x+1}=162:2=81=3^4$

$\Rightarrow x+1=4$

$\Rightarrow x=3$

\(\Rightarrow6x=5312\)

\(\Rightarrow x=5312:6\)

\(\Rightarrow x=885,3333333\)

tíc nha

\(2.3x=10.312+8.274\)

\(=2.3x=3120+2192\)

\(2.3x=5312\)

\(3x=5312:2\)

\(3x=2656\)

\(x=2656:3\)

\(x=\frac{2556}{3}\)

\(3^x+2.3^{x-2}=297\)

\(\Rightarrow3^x\left(1+2.3^{-2}\right)=297\)

\(\Rightarrow3^x\left(1+2.\dfrac{1}{3^2}\right)=297\)

\(\Rightarrow3^x\left(1+\dfrac{2}{9}\right)=297\)

\(\Rightarrow3^x\left(\dfrac{9}{9}+\dfrac{2}{9}\right)=297\)

\(\Rightarrow3^x.\dfrac{11}{9}=297\)

\(\Rightarrow3^x=297:\dfrac{11}{9}=297.\dfrac{9}{11}=243\)

\(\Rightarrow3^x=3^5\)

\(\Rightarrow x=5\) (thỏa mãn)

\(3^x+2.3^{x-2}=297\)

\(3^x+2.3^x:3^2=297\)

\(3^x\left(1+\dfrac{2}{9}\right)=297\)

\(3^x.\dfrac{11}{9}=297\)

\(3^x=297:\dfrac{11}{9}=243=3^5\)

⇒\(x=5\)

\(a,121-\left(115+x\right)=3x-\left(25-9-5x\right)-8\\ 121-115-x=3x-25+9+5x-8\\ 6-x=8x-24\\ 8x+x=-24-6\\ 9x=-30\\ x=-\dfrac{30}{9}=-\dfrac{10}{3}\\ ----\\ b,2^{x+2}.3^{x+1}.5^x=10800\\ \left(2.3.5\right)^x.2^2.3=10800\\ 30^x.12=10800\\ 30^x=\dfrac{10800}{12}=900=30^2\\ Vậy:x=2\)