5.3^x = 5.3⁴

=> x = 4

5.3⁴ = 7.3⁵ - 2.3⁵

       = 3⁵ . (7 - 2)

       = 5. 3⁵

  => 3^x = 3⁵

=> x = 5

a) Ta có: \(5\cdot3^x=5\cdot3^4\)

\(\Leftrightarrow3^x=3^4\)

hay x=4

Lời giải:

1.

$3^{x+2}+4.3^{x+1}=7.3^6$

$3^{x+1}.3+4.3^{x+1}=7.3^6$

$3^{x+1}(3+4)=7.3^6$

$3^{x+1}.7=7.3^6$

$\Rightarrow 3^{x+1}=3^6$

$\Rightarrow x+1=6$

$\Rightarrow x=5$

2.

$5^{x+4}-3.5^{x+3}=2.5^{11}$

$5^{x+3}.5-3.5^{x+3}=2.5^{11}$

$5^{x+3}(5-3)=2.5^{11}$

$2.5^{x+3}=2.5^{11}$

$\Rightarrow 5^{x+3}=5^{11}$

$\Rightarrow x+3=11$

$\Rightarrow x=8$

3.

$4^{x+3}-3.4^{x+1}=13.4^{11}$

$4^{x+1}.4^2-3.4^{x+1}=13.4^{11}$

$4^{x+1}.16-3.4^{x+1}=13.4^{11}$

$13.4^{x+1}=13.4^{11}$

$\Rightarrow 4^{x+1}=4^{11}$

$\Rightarrow x+1=11$
$\Rightarrow x=10$

1) \(7.4^x=7.4^3\Leftrightarrow4^x=4^3;x=3\)

2) \(\frac{3}{2.5^x}=\frac{3}{2.5^{12}}\Leftrightarrow5^x=5^{12};x=12\)

\(2^x=2.2^8=2^9;x=9\)

4) \(5.3^x=7.3^5-2.3^5\Leftrightarrow5.3^x=3^5.\left(7-2\right)\)

\(\Leftrightarrow3^5.x=3^5.5;x=5\)

a) \(-12\left(x-5\right)+7\left(3-x\right)=5\)

\(-12x+60+21-7x=5\)

\(-19x=5-60-21\)

\(-19x=-76\)

\(x=4\)

vậy \(x=4\)

tương tự 

c, \(5^{x+4}-3\cdot5^{x+3}=2\cdot5^{11}\)

\(\Leftrightarrow5^{x+3}\cdot5-3\cdot5^{x+3}=2\cdot5^{11}\)

\(\Leftrightarrow5^{x+3}\left(5-3\right)=2\cdot5^{11}\)

\(\Leftrightarrow5^{x+3}\cdot2=2\cdot5^{11}\)

\(\Leftrightarrow5^{x+3}=5^{11}\)

\(\Leftrightarrow x+3=11\)

\(\Leftrightarrow x=8\)

Vậy x = 8

d, \(2^x+2^{x+1}+2^{x+2}+2^{x+3}+2^{x+4}+2^{x+5}=480\)

\(\Leftrightarrow2^x\left(1+2+2^2+2^3+2^4+2^5\right)=480\)

\(\Leftrightarrow2^x\cdot63=480\)

\(\Leftrightarrow2^x=\frac{160}{21}\)

\(\Leftrightarrow x\approx2,93\)

bạn nào chơi ff ko?

bn nào trả lời hộ mk ik

đang gấp !!!

1) Tìm số nguyên x, biết : 

a) 3^{x + 2} + 4 . 3^{x + 1} = 7.3⁶

3^{x + 1} ( 3 + 4) = 7.3⁶

3^{x + 1} .7 = 7.3⁶

=> x + 1 = 6

=> x = 5

b) 4^{x + 3} - 3.4^{x + 1} = 13 . 4¹¹

4^{x + 1} ( 4² - 3) = 13 . 4¹¹

4^{x + 1} . 13 = 13 . 4¹¹

=> x + 1 = 11

=> x = 10