Question

tìm x

a , \(2.3^{x+2}+4.3^{x+1}=3^6.10\)

b, \(\left(\frac{1}{3}+\frac{1}{6}\right).2^{x+4}-2^x=2^{13}-2^{16}\)

Answer 1

a, Ta có \(2.3^{x+2}+4.3^{x+1}=3^6.10\)

\(\Rightarrow2.3.3^{x+1}+4.3^{x+1}=3^6.10\)

\(\Rightarrow3^{x+1}.\left(6+4\right)=3^6.10\)

\(\Rightarrow3^{x+1}.10=3^6.10\)

\(\Rightarrow3^{x+1}=3^6\)

\(\Rightarrow x+1=6\)

\(\Rightarrow x=5\)

b,\(\left(\frac{1}{3}+\frac{1}{6}\right).2^{x+4}-2^x=2^{13}-2^{16}\)

\(\Rightarrow\frac{1}{2}.2^{x+4}-2^x=2^{13}.\left(1-2^3\right)\)

\(\Rightarrow2^{x+3}-2^x=2^{13}.\left(1-2^3\right)\)

\(\Rightarrow2^x.\left(2^3-1\right)=2^{13}.\left(1-2^3\right)\)

\(\Rightarrow2^x.\left(2^3-1\right)=-2^{13}.\left(2^3-1\right)\)

\(\Rightarrow2^x=2^{-13}\)

\(\Rightarrow x=-13\)

Answer 2

A ) 2 . 3^x+2 + 4 . 3³⁺¹ = 3⁶ . 10

      2 . 3^x . 9 + 4 . 3^x . 3 = 729 .10

         18 . 3^x + 12 . 3^x = 243 . 3 . 10

                        30 . 3^x = 243 . 30

                               3^x = 243

                                 x = 5