Question

5.3\(^{x+2}\) -5=2\(^4\) .5\(^2\)

Answer 1

\(5\cdot3^{x+2}-5=2^4\cdot5^2\)

\(\Rightarrow5\left(3^{x+2}-1\right)=2^4\cdot5^2\)

\(\Rightarrow3^{x+2}-1=\dfrac{2^4\cdot5^2}{5}\)

\(\Rightarrow3^{x+2}-1=16\cdot5\)

\(\Rightarrow3^{x+2}-1=80\)

\(\Rightarrow3^{x+2}=80+1\)

\(\Rightarrow3^{x+2}=81\)

\(\Rightarrow3^{x+2}=3^4\)

\(\Rightarrow x+2=4\)

\(\Rightarrow x=2\)

Vậy: x = 2 

Answer 2

\(5\cdot3^{x+2}-5=2^4\cdot5^2\\\Rightarrow 5\cdot(3^{x+2}-1)=5\cdot(2^4\cdot5)\\\Rightarrow3^{x+2}-1=2^4\cdot5\\\Rightarrow3^{x+2}-1=16\cdot5\\\Rightarrow3^{x+2}-1=80\\\Rightarrow3^{x+2}=80+1\\\Rightarrow3^{x+2}=81\\\Rightarrow3^{x+2}=3^4\\\Rightarrow x+2=4\\\Rightarrow x=4-2\\\Rightarrow x=2\\Vậy:x=2\)