\(5^x-2-3^2=2^4-\left(2^8x2^4-2^{10}x2^2\right)\)

\(5^x-2-3^2=2^4-\left(2^{8+4}-2^{10+2}\right)\)

\(5^x-2-3^2=2^4-\left(2^{12}-2^{12}\right)\)

\(5^x-2-3^2=2^4-0\)

\(5^x-2-3^2=2^4\)

\(5^x-2-9=16\)

\(5^x-2=16+9\)

\(5^x-2=25\)

\(5^x=25+2\)

\(5^x=27\)

Bởi vì 27 không phân tích được 1 số có số mũ là 2

\(\Rightarrow\) Không tồn tại x

\(5^{x-2}-9=16-\left(256.16-1024.4\right)\)

\(\Rightarrow5^{x-2}-9=16-\left(4096-4096\right)\)

\(\Rightarrow5^{x-2}-9=16-0\)

\(\Rightarrow5^{x-2}-9=16\)

\(\Rightarrow5^{x-2}=25\)

\(\Rightarrow x-2=25:5\)

\(\Rightarrow x-2=3\)

\(\Rightarrow x=5\)

\(5^{x-2}-3^2=2^4-\left(2^8\cdot2^4-2^{10}\cdot2^2\right)\)

\(\Rightarrow5^{x-2}-3^2=2^4-\left(2^{12}-2^{12}\right)\)

\(\Rightarrow5^{x-2}-9=16-0\)

\(\Rightarrow5^{x-2}=16+9\)

\(\Rightarrow5^{x-2}=25\)

\(\Rightarrow5^{x-2}=5^2\)

\(\Rightarrow x-2=2\)

\(\Rightarrow x=2+2\)

\(\Rightarrow x=4\)

Vậy: x=4

3 giờ 25 phút x 7 = 23 giờ 55 phút
4 giờ 6 phút x 8 = 32 giờ 48 phút
1 giờ 30 phút x 4 = 6 giờ

3 giờ 25 phút x 7 = 23 giờ 55 phút
4 giờ 6 phút x 8 = 32 giờ 48 phút
1 giờ 30 phút x 4 =  6 giờ

 23 giờ 55 phút
 32 giờ 48 phút
 6 giờ

a) \(2.\left(x+\frac{2}{5}\right)+1\frac{1}{4}=\frac{11}{20}\)

\(2.\left(x+\frac{2}{5}\right)+\frac{5}{4}=\frac{11}{20}\)

\(2.\left(x+\frac{2}{5}\right)=\frac{-7}{10}\)

\(x+\frac{2}{5}=\frac{-7}{20}\)

\(x=\frac{-13}{20}\)

Vậy \(x=\frac{-13}{20}\)

b)\(x-1\frac{1}{8}-\frac{2}{3}x-\frac{5}{6}x=75\%\)

  \(\left(x-\frac{2}{3}x-\frac{5}{6}x\right)-\frac{9}{8}=\frac{3}{4}\)

\(\frac{-1}{2}x-\frac{9}{8}=\frac{3}{4}\)

\(\frac{-1}{2}x=\frac{15}{8}\)

\(x=\frac{-15}{4}\)

Vậy \(x=\frac{-15}{4}\)

\(a,2.\left(x+\frac{2}{5}\right)+1\frac{1}{4}=\frac{11}{20}\)

\(2.\left(x+\frac{2}{5}\right)+\frac{5}{4}=\frac{11}{20}\)

\(2.\left(x+\frac{2}{5}\right)=\frac{11}{20}-\frac{5}{4}\)

\(2.\left(x+\frac{2}{5}\right)=\frac{-7}{10}\)

\(x+\frac{2}{5}=\frac{-7}{10}:2\)

\(x+\frac{2}{5}=\frac{-7}{20}\)

\(x=\frac{-7}{20}-\frac{2}{5}\)

\(x=\frac{-3}{4}\)

A = 9x² + 6x + 15

A = [(3x + 6x + 1] + 14

A = (3x + 1)² + 14 \(\ge\)14

Dấu = xảy ra \(\Leftrightarrow\)3x + 1 = 0

                        \(\Rightarrow\)3x = - 1

                       \(\Rightarrow\)x = - 1 / 3

Min A = 14 \(\Leftrightarrow\)x = - 1 / 3

1, Tìm x :

a, \(x^7.x^5=3^{12}\)

\(\Rightarrow x^{12}=3^{12}\)

\(\Rightarrow x=3\)

Vậy x = 3

b, \(\left(x+1\right)^4=5^8\div25^4\)

\(\left(x+1\right)^4=5^8\div\left(5^2\right)^4\)

\(\left(x+1\right)^4=5^8\div5^8\)

\(\left(x+1\right)^4=1\)

\(\Rightarrow x\in\left\{0;1\right\}\)

Vậy \(x\in\left\{0;1\right\}\)

c, \(x^6=x\)

\(\Rightarrow x^6-x=0\)

\(\Rightarrow x.x^5-x.1=0\)

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

x = 0 hoặc x⁵ - 1 = 0

x = 0 hoặc x⁵= 1

x = 0 hoặc x⁵ = 1

\(\Rightarrow x\in\left\{0;1\right\}\)

Vậy \(x\in\left\{0;1\right\}\)

2, Tính :

\(\left(4^{20}+4^{15}\right)\div\left(4^{10}+4^5\right)\) 

\(=4^{15}.\left(4^5+1\right)\div4^5.\left(4^5+1\right)\)

\(=4^{15}\div4^5\)

\(=4^{10}\)

Vậy giá trị biểu thức trên bằng 4¹⁰

\(A=2^0+2^1+2^2+...+2^{2016}\)

\(2A=2+2^2+2^3+...+2^{2017}\)

\(2A-A=\left(2+2^2+2^3+...+2^{2017}\right)-\left(2^0+2^1+2^2+...+2^{2016}\right)\)

\(\Rightarrow A=2^{2017}-1\)

Vậy : \(A=2^{2017}-1\)

\(x^7\times x^5=3^{12}\)

\(x^{12}=3^{12}\)

\(x=3\)

^^

\(\left(x+1\right)^4=\frac{5^8}{25^4}\)

\(\left(x+1\right)^4=\frac{\left(5^2\right)^4}{\left(5^2\right)^4}\)

\(\left(x+1\right)^4=1\)

\(\left[\begin{array}{nghiempt}x+4=1\\x+4=-1\end{array}\right.\)

\(\left[\begin{array}{nghiempt}x=1-4\\x=-1-4\end{array}\right.\)

\(\left[\begin{array}{nghiempt}x=-3\\x=-5\end{array}\right.\)

^^

\(x^6=x\)

\(\left[\begin{array}{nghiempt}x=1\\x=-1\\x=0\end{array}\right.\)

^^

\(\frac{4^{20}+4^{15}}{4^{10}+4^5}=\frac{4^{15}\times\left(4^5+1\right)}{4^5\times\left(4^5+1\right)}=4^{10}\)

^^

\(A=2^0+2^1+2^2+...+2^{2016}\)

\(2A=2^1+2^2+2^3+...+2^{2017}\)

\(2A-A=\left(2^1+2^2+2^3+...+2^{2017}\right)-\left(2^0+2^1+2^2+...+2^{2016}\right)\)

\(A=2^{2017}-1\)

\(\text{Cx khá đơn giản nhưng a giải chi tiết luôn nha}\)

\(1.\)

\(5\left(x+4\right)=25x\)

\(\Leftrightarrow5x+20=25x\)

\(\Leftrightarrow5x-25x=-20\)\(\text{(chuyển vế)}\)

\(\Leftrightarrow-20x=-20\)

\(\Leftrightarrow x=1\)

\(2.\)

\(-\frac{3}{6}=\frac{25}{2x-1}\)

\(\Leftrightarrow-\frac{1}{2}=25.\frac{1}{2x-1}\)

\(\Leftrightarrow\frac{1}{2x-1}=-\frac{1}{2}:25=-\frac{1}{50}\)

\(3.\)\(\text{(tương tự)}\)

\(\Leftrightarrow-50=2x-1\)\(\text{(nhân chéo)}\)

\(\Leftrightarrow x=-50+1=-49\)

\(4.\)

\(5\left(x-4\right)=3x+8\)

\(\Leftrightarrow5x-20=3x+8\)

\(\Leftrightarrow5x-3x=20+8\)

\(\Leftrightarrow2x=28\)

\(\Leftrightarrow x=28:2=14\)

1) 5.(x+4)=25x

5x+20=25x

20=25x-5x

20=20x

x=1

2) \(\frac{-3}{6}=\frac{25}{2x-1}\)

-3.(2x-1)=6.25                

-6x+3=150

-6x=147

x=-24,5

câu 3,4 lm tương tự nha Nhớ đấy!!!!

\(\left(x-2\right)\left(4x-20\right)=0\\ \Rightarrow\left[{}\begin{matrix}x-2=0\\4x-20=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=2\\4x=20\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=2\\x=5\end{matrix}\right.\\ \left(x-5\right)\left(25-5x?\right)=0\\ \Rightarrow\left[{}\begin{matrix}x-5=0\\25-5x=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=5\\5x=25\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=5\\x=5\end{matrix}\right.\\ \left(x-4\right)\left(2x-8\right)\\ \Rightarrow\left[{}\begin{matrix}x-4=0\\2x-8=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=4\\2x=8\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=4\\x=4\end{matrix}\right.\)

a,(x-2)(4x-20)=0

=>x-2=0 hoặc 4x-20=0

=>x=2 hoặc x=5

b,(x-5)(25-5)=0

=>x-5=0  ( vì 25-5 ≠0)

=>x=5

c,(x-4)(2x-8)=0

=>x-4=0 hoặc 2x-8=0

=>x=4 

\(\left(x-2\right)\left(4x-20\right)=0\\ \Rightarrow\left[{}\begin{matrix}x-2=0\\4x-20=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=2\\4x=20\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=2\\x=5\end{matrix}\right.\)

Vậy x={2;5}

________________________

\(\left(x-5\right)\left(25-5\right)=0\\ \Rightarrow\left(x-5\right)20=0\\ \Rightarrow x-5=0\\ \Rightarrow x=5\)

Vậy x=5

_____________________

\(\left(x-4\right)\left(2x-8\right)=0\\ \Rightarrow2x-8=x-4\\ \Rightarrow2x-8-x=-4\\ \Rightarrow x-8=-4\\ \Rightarrow x=-4+8\\ \Rightarrow x=4\)