a) 5^{x + 1} - 2.5^x = 75

<=> 5^x.5 - 2.5^x = 75

<=> 5^x.3 = 75

<=> 5^x = 25

<=> 5^x = 5²

<=> x = 2

Vậy x = 2

b) 9^{x + 1} -  5.3^2x = 324

<=> (3²)^{x + 1} - 5.3^2x = 324

<=> 3^{2x + 2} - 5.3^2x = 324

<=> 3^2x.3² - 5.3^2x = 324

<=> 3^2x . 4 = 324

<=> 3^2x = 81

<=> 3^2x = 3⁴

<=> 2x = 4

<=> x = 2

Vậy x = 2

UIUYI

9^x+1-5.3^2x=324

=>9^x.9-(3²)^x.5=324

=>9^x.9-9^x.5=324

=>9^x(9-5)=324

=>9^x.4=324

=>9^x=324:4

=>9^x=81

=>9^x=9²

=>x=2

vậy x=2

\(9^{x+1}-5.3^{2x}=324=>9^x.9-5.\left(3^2\right)^x=324=>\left(3^2\right)^x.9-5.\left(3^2\right)^x=324\)

\(=>3^{2x}.\left(9-5\right)=324=>3^{2x}=\frac{324}{4}=81=3^4=>2x=4=>x=2\)

vậy x=2

tick nhé

a) \(5^{x+1}-2.5^x=375\)
\(\Rightarrow5^x\left(5-2\right)=375\)
\(\Rightarrow5^x.3=375\)
\(\Rightarrow5^x=125=5^3\)
\(\Rightarrow x=3\)
b) \(9^{x+1}-5.3^{2x}=324\)
\(\Rightarrow3^{2\left(x+1\right)}-5.3^{2x}=324\)
\(\Rightarrow3^2\left(3^{x+1}-5.3^x\right)=324\)
\(\Rightarrow9.3^x\left(3-5\right)=324\)
\(\Rightarrow3^x.\left(-2\right)=36\)
\(\Rightarrow3^x=-18=3^2.\left(-2\right)\)(vô lí vì 3^x không chia hết cho 2)
c) \(\left(1-x\right)^5=32=2^5\)
\(\Rightarrow1-x=2\)
\(\Rightarrow x=-1\)
d) \(3.5^{2x+1}-3.25^x=300\)
\(\Rightarrow3\left(5^{2x}.5-5^{2x}\right)=300\)
\(\Rightarrow5^{2x}\left(5-1\right)=100\)
\(\Rightarrow5^{2x}.4=100\)
\(\Rightarrow5^{2x}=25=5^2\)
\(\Rightarrow2x=2\)
\(\Rightarrow x=1\)
 

\(9^{x+1}+5.3^{2x}=324\)

\(9^x.9+5.\left(3^2\right)^x=324\)

\(9^x.9+5.9^x=324\)

\(9^x.\left(5+9\right)=324\)

\(9^x.14=324\)

\(9^x=\frac{324}{14}\)

\(\Rightarrow x\in\varnothing\)

kb vs mk nha mk cx là fan conan