\(5^{x+4}-3.5^{x+3}=2.5^{11}\)

\(5^{x+3}\left(5-3\right)=2.5^{11}\)

\(5^{x+3}.2=2.5^{11}\)

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

\(x+3=11\)

\(x=8\)

\(4^{x+3}-3.4^{x+1}=13.4^{11}\)

\(4^{x+1}\left(4^2-3\right)=13.4^{11}\)

\(4^{x+1}.13=13.4^{11}\)

\(4^{x+1}=4^{11}\)

\(x+1=11\)

\(x=10\)

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

làm ơn giúp mình ,bạn nào làm nhanh đúng mình chọn cho nhanh nha mọi người

nhanh nha mọi người

T.T

Bài làm

2².4⁴.2⁶.2.2=2².2⁸.2⁶.2²=2¹⁸

2.2³.2⁷.2⁴=2¹⁵

3².3=3³=27

3⁴.3³.3=3⁸

3.3⁵.3⁴.3²=3¹²

3.3⁶.3⁷.3⁴=3¹⁸

4.4³=4⁴

4⁵.4.4⁷=4¹³

4.4³.4⁵.4⁶=4¹⁵

5.5⁶=5⁷

5.5⁴=5⁵

5.5².5⁴=5⁷

5.5³.5⁴.5⁶=5¹⁴

5.5⁶.5⁴.5³=5¹⁴

x.x²=x³

x.x³.x⁵=x⁹

a.a⁴=a⁵

a.a².a⁴.a⁵.a⁷=a¹⁹

a.a³.a⁵.a⁶=a¹⁵

a.a⁴.a.a⁵.a⁶.a=a¹⁸

x.x³.x⁴=x⁸

x⁵.x⁴.x.x⁷.x⁶=x²³

7.7²=7³

7.7².7⁴.7⁵=7¹²

7³.7⁵.7⁴.7=7¹³

7².7.7⁶.7⁶.7³=7¹⁸

10.10²=10³

10.100.10³=10⁶

10.100.10⁴.1000=10¹⁰

10².10⁴.100.1000=10¹¹

Tk nha !

a)\(\left(-3\right)^{x+3}=-\frac{1}{27}\)

\(\left(-3\right)^{x+3}=\left(-\frac{1}{3}\right)^3\)

\(\left(-3\right)^{x+3}=\left(-\frac{3^0}{3^1}\right)^3\)

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

\(\left(-3\right)^{x+3}=\left(-3\right)^{-3}\)

\(\Rightarrow x+3=-3\)

\(\Rightarrow x=-6\)

b)\(\left(-6\right)^{2x+2}=\frac{1}{36}\)

\(\left(-6\right)^{2x+2}=\left(-\frac{1}{6}\right)^2\)

\(\left(-6\right)^{2x+2}=\left(-\frac{6^0}{6^1}\right)^2\)

\(\left(-6\right)^{2x+2}=\left(-6^{-1}\right)^2\)

\(\left(-6\right)^{2x+2}=\left(-6\right)^{-2}\)

\(\Rightarrow2x+2=-2\)

\(\Rightarrow2x=-4\)

\(\Rightarrow x=-2\)

c)\(\left(-3\right)^{x+5}=\frac{1}{81}\)

\(\left(-3\right)^{x+5}=\left(-\frac{1}{3}\right)^4\)

\(\left(-3\right)^{x+5}=\left(-\frac{3^0}{3^1}\right)^4\)

\(\left(-3\right)^{x+5}=\left(-3^{-1}\right)^4\)

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

\(\Rightarrow x+5=-4\)

\(\Rightarrow x=-9\)

d)\(\left(\frac{1}{9}\right)^x=\left(\frac{1}{27}\right)^6\)

\(\left[\left(\frac{1}{3}\right)^2\right]^x=\left[\left(\frac{1}{3}\right)^3\right]^6\)

\(\left(\frac{1}{3}\right)^{2x}=\left(\frac{1}{3}\right)^{18}\)

\(\Rightarrow2x=18\)

\(\Rightarrow x=9\)

e)\(\left(\frac{4}{9}\right)^x=\left(\frac{8}{27}\right)^6\)

\(\left[\left(\frac{2}{3}\right)^2\right]^x=\left[\left(\frac{2}{3}\right)^3\right]^6\)

\(\left(\frac{2}{3}\right)^{2x}=\left(\frac{2}{3}\right)^{18}\)

\(\Rightarrow2x=18\)

\(\Rightarrow x=9\)

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

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

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

\(5^{x+3}\cdot2=2\cdot5^{11}\)

\(\Rightarrow5^{x+3}=5^{11}\)

\(\Rightarrow x+3=11\)

\(\Rightarrow x=8\)

r)\(4\cdot3^{x-1}+2\cdot3^{x+2}=4\cdot3^6+2\cdot3^9\)

\(4\cdot3^x:3+2\cdot3^x\cdot9=4.3^7:3+2\cdot3^7\cdot9\)

\(3^x\left(4:3+2\cdot9\right)=3^7\left(4:3+2\cdot9\right)\)

\(\Rightarrow3^x=3^7\)

\(\Rightarrow x=7\)