5.3^x=5.3⁴

<=> 3^x=3⁴( chia cả hai vế cho 5)

<=> x=4

Câu thứ hai viết lại đề

5^4-3/100=1/20

3^3+2+1/3*13=3^5/13

5.3^7-5/5.3^5-3=1

2^15+14+13/2^13+12+11=2^6

Câu a:

\(\frac{x+5}{x+9}\) = \(\frac{x+4}{x+3}\)

(\(x\) + 5)(\(x+3\)) = (\(x+4\))(\(x+9\))

\(x^2\) + 3\(x\) + 5\(x\) + 15 = \(x^2\) + 9\(x\) + 4\(x\) + 36

\(x^2+3x+5x\) - \(x^2-9x\) - 4\(x\) = 36 - 15

(\(x^2-x^2\)) + (\(3x+5x\) - 9\(x-4x\)) = 21

0 + (8\(x\) - 9\(x\) - 4\(x\)) = 21

-\(x-4x\) = 21

-5\(x\) = 21

\(x\) = 21 : (-5)

\(x\) = - \(\frac{21}{5}\)

Vậy \(x=-\frac{21}{5}\)

5\(\frac{8}{17}\) : x - (\(\frac{8}{17}\)) : x + 3\(\frac{1}{17}\): 17\(\frac13\) = \(\frac{4}{17}\)

(5\(\frac{8}{17}\) - \(\frac{8}{17}\)) : x + \(\frac{52}{17}\) : \(\frac{52}{3}\) = \(\frac{4}{17}\)

5:x + \(\frac{52}{17}\times\) \(\frac{3}{52}\) = \(\frac{4}{17}\)

5 : x + \(\frac{3}{17}\) = \(\frac{4}{17}\)

5 : x = \(\frac{4}{17}\) - \(\frac{3}{17}\)

5 : x = \(\frac{1}{17}\)

x = 5 : \(\frac{1}{17}\)

x = 5 x 17

x = 85

Vậy x = 85

1/1.4 + 1/4.7 + ...+1/x(x+3) = 6/19

3/1.4 + 3/4.7 +..+3/x(x+3) = 18/19

1/1 - 1/4+ 1/4 - 1/7 +...+1/x-1/(x+3) = 1 - 1/19

1- 1/(x+3) = 1 - 1/19

1/(x+3) = 1/19

x + 3 = 19

x = 19 - 3

x = 16

Vậy x = 16

a) (\(6\frac{2}{7}.x+\frac{3}{7}\))=-1.\(\frac{11}{5}+\frac{3}{7}\)

(\(6\frac{2}{7}.x+\frac{3}{7}\))=\(\frac{-62}{35}\)

\(\frac{44}{7}.x\)=\(\frac{-62}{35}-\frac{3}{7}\)

\(\frac{44}{7}.x=\frac{-77}{35}\)

x=\(\frac{-77}{35}:\frac{44}{7}\)=\(\frac{539}{1540}\)

(6\(\frac27x\) + \(\frac37\)) : 2\(\frac15\) - \(\frac37\) = - 1

(\(\frac{44}{7}x\) + \(\frac37\)) : \(\frac{11}{5}\) = - 1 + \(\frac37\)

(\(\frac{44}{7}x+\) \(\frac37\)) : \(\frac{11}{5}\) = - \(\frac77+\frac37\)

\(\frac{44x+3}{7}\) : \(\frac{11}{5}\) = - \(\frac47\)

(44\(x\) + 3) : \(\frac{11}{5}\) = - 4

44\(x\) + 3 = - 4 x \(\frac{11}{5}\)

44\(x\) + 3 = - \(\frac{44}{5}\)

44\(x\) = - \(\frac{44}{5}\) - 3

44\(x\) = - \(\frac{59}{5}\)

\(x=-\frac{59}{5}:44\)

\(x\) = - \(\frac{59}{250}\)

Vậy \(x\) = - \(\frac{59}{250}\)

\(f\)) \(32^{-x}.16^x=1024\)

\(\left(2\right)^{-5x}.2^{4x}=2^{10}\)

\(\Leftrightarrow2^{4x-5x}=2^{10}\)

\(\Leftrightarrow2^{-x}=2^{10}\)

\(\Leftrightarrow-x=10\)

\(\Leftrightarrow x=-10\)

\(g\)) \(3^{x-1}.5+3^{x-1}=162\)

\(3^{x-1}.\left(5+1\right)=162\)

\(3^{x-1}.6=162\)

\(3^{x-1}=162:6\)

\(3^{x-1}=27\)

\(\Leftrightarrow3^{x-1}=3^3\)

\(\Leftrightarrow x-1=3\)

\(\Leftrightarrow x=4\)

\(h\)) \(\left(2x-1\right)^6=\left(2x-1\right)^8\)

\(\Leftrightarrow\left(2x-1\right)^6-\left(2x-1\right)^8=0\)

\(\Leftrightarrow\left(2x-1\right)^6-\left(2x-1\right)^6.\left(2x-1\right)^2=0\)

\(\Leftrightarrow\left(2x-1\right)^6.\left[1-\left(2x-1\right)^2\right]=0\)

\(\Leftrightarrow\orbr{\begin{cases}\left(2x-1\right)^6=0\\1-\left(2x-1\right)^2=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}2x-1=0\\\left(2x-1\right)^2=1\end{cases}}\)\(\Leftrightarrow\orbr{\begin{cases}2x=1\\\left(2x-1\right)^2=\left(1,-1\right)^2\end{cases}}\)

\(\Leftrightarrow\hept{\begin{cases}x=\frac{1}{2}\\2x-1=-1\\2x-1=1\end{cases}}\)\(\Leftrightarrow\hept{\begin{cases}x=\frac{1}{2}\\2x=0\\2x=2\end{cases}}\)\(\Leftrightarrow\hept{\begin{cases}x=\frac{1}{2}\\x=0\\x=1\end{cases}}\)

\(i\)) \(5^x+5^{x+2}=650\)

\(5^x.\left(1+5^2\right)=650\)

\(5^x.26=650\)

\(5^x=650:26\)

\(5^x=25\)

\(\Leftrightarrow5^x=5^2\)

\(\Leftrightarrow x=2\)

\(\frac{7^{x+2}+7^{x+1}+7^x}{57}=\frac{5^{2x}+5^{2x+1}+5^{2x+3}}{131}\)

\(\Rightarrow\frac{7^x.7^2+7^x.7^1+7^x}{57}=\frac{5^{2x}+5^{2x}.5+5^{2x}.5^3}{131}\)

\(\Rightarrow\frac{7^x.\left(7^2+7+1\right)}{57}=\frac{5^{2x}.\left(1+5+5^3\right)}{131}\)

\(\Rightarrow\frac{7^x.57}{57}=\frac{5^{2x}.131}{131}\)

\(\Rightarrow7^x=5^{2x}\)

Bạn tự làm phần còn lại nhé