Question

\(5^x-5^{x+3}=3100\)                                                                                             

\(5^x\times\left(5^3\right)^4=625\)

\(\left(3x+1\right)^2=\frac{49}{64}\)

\(\left(8x-1\right)^{2n+2}=7^{2n+2}\left(n\in N\right)\)

\(2^{x+1}\times3^y=12^x\)

\(10^x:5^y=20^y\)

Các bạn giúp mk vói nhé. Tặng 3tick

 

Answer 1

5^x-5^x+3=3100

5^x-5^x.5³=3100

5^x(1-5³)=3100

5^x. (-124)=3100

5^x =-25

5^x=-5²

....

Answer 2

5^x . (5³)⁴=625

5^x.5¹²=625

5^x=5⁴:5¹²

.. tự làm típ

Answer 3

(3x+1)²= \(\frac{49}{64}\)

\(\Rightarrow\orbr{\begin{cases}3x+1=\frac{7}{8}\\3x+1=\frac{-7}{8}\end{cases}}\)

. tự làm típ

Answer 4

(8x-1)²ⁿ⁺²=7²ⁿ⁺²

vì 2n+2 chẵn\(\forall x\in Q\)

=>\(\orbr{\begin{cases}8x-1=7\\8x-1=-7\end{cases}}\)

tự làm típ

Answer 5

a, Ta có : 

\(5^x-5^{x+3}=3100\)

\(\Rightarrow5^x\left(1-5^3\right)=3100\)

\(\Rightarrow5^x.\left(-124\right)=3100\Rightarrow5^x=-25\)( Vô lí )

b, Ta có : 

\(5^x.\left(5^3\right)^4=625\Rightarrow5^x.5^{12}=5^4\Rightarrow5^x=\frac{5^4}{5^{12}}=\frac{1}{5^8}\Rightarrow x=-8\)

c,\(\left(3x+1\right)^2=\frac{49}{64}\Rightarrow\left(3x+1\right)^2=\left(\frac{7}{8}\right)^2\Rightarrow\orbr{\begin{cases}3x+1=\frac{7}{8}\\3x+1=-\frac{7}{8}\end{cases}\Rightarrow\orbr{\begin{cases}x=-\frac{1}{24}\\x=-\frac{5}{8}\end{cases}}}\)

d, \(\left(8x-1\right)^{2n+2}=7^{2n+2}\Rightarrow\orbr{\begin{cases}8x-1=7\\8x-1=-7\end{cases}\Rightarrow\orbr{\begin{cases}x=1\\x=-\frac{3}{4}\end{cases}}}\)

e,\(2^{x+1}.3^y=12^x\Rightarrow2^x.2.3^y=3^x.2^{2x}\Rightarrow2.3^y=3^x.2^x\Rightarrow x=y=1\)

d,\(10^x:5^y=20^y\Rightarrow10^x=20^y.5^y=\left(20.5\right)^y=100^y=10^{2y}\Rightarrow x=2y\left(x,y\inℤ\right)\)