Question

Tìm số nguyên x, nếu biết

a, \((\dfrac{1}{2}-\dfrac {1}{6})3^x +3^{x+2}= 3^{16}+3^{13}\)

b, \((\dfrac {1}{2}-\dfrac{1}{3}).6^x +6^{x+2}= 6^{15}+6^{18}\)

c, \((\dfrac{1}{3}+\dfrac{1}{6})2^{x+3} -2^x = 2^{22}-2^{20}\)

Answer 1

a/ \(\frac{1}{3}.3^x+3^{x+2}=3^{16}+3^{13}\)

\(\Leftrightarrow3^{x-1}+3^{x+2}=3^{13}+3^{16}\)

\(\Leftrightarrow3^{x-1}\left(1+3^3\right)=3^{13}\left(1+3^3\right)\)

\(\Leftrightarrow3^{x-1}=3^{13}\Rightarrow x-1=13\Rightarrow x=14\)

b/ \(\frac{1}{6}6^x+6^{x+2}=6^{15}+6^{18}\)

\(\Leftrightarrow6^{x-1}+6^{x+2}=6^{15}+6^{18}\)

\(\Leftrightarrow6^{x-1}\left(1+6^3\right)=6^{15}\left(1+6^3\right)\)

\(\Rightarrow x=16\)

c/ \(\frac{1}{2}2^{x+3}-2^x=2^{22}-2^{20}\)

\(\Leftrightarrow2^x\left(2^2-1\right)=2^{20}\left(2^2-1\right)\)

\(\Rightarrow x=20\)