\(4^x+4^{x+3}=4160\)

\(4^x\times\left(1+4^3\right)=4160\)

\(4^x\times\left(1+64\right)=4160\)

\(4^x\times65=4160\)

\(4^x=\frac{4160}{65}\)

\(4^x=64\)

\(4^x=4^3\)

\(x=3\)

\(4^x+4^{x+3}=4160\)

\(\Rightarrow4^x+4^x.4^3=4160\)

\(\Rightarrow4^x.\left(1+4^3\right)=4160\)

\(\Rightarrow4^x.65=4160\)

\(\Rightarrow4^x=64\)

\(\Rightarrow4^x=4^3\)

\(\Rightarrow x=3\)

Vậy \(x=3\)

4^x+4^x+3=4160

=>4^x+4^x.4³=4160

=>4^x(1+64)=4160

=>65.4^x=4160

=>4^x=64

=>x=3

Vậy x=3

\(4^x+4^{x+3}=4160\)

\(\Rightarrow4^x+4^x.4^3=4160\)

\(\Rightarrow4^x.\left(1+4^3\right)=4160\)

\(\Rightarrow4^x.65=4160\)

\(\Rightarrow4^x=64\)

\(\Rightarrow x=3\)

\(4^x+4^x.4^3=4160\)

\(\Leftrightarrow4^x\left(1+64\right)=4160\)

\(\Leftrightarrow4^x=4160:65\)

\(\Leftrightarrow4^x=64=4^3\)

\(\Leftrightarrow x=3\)

\(4^{x+3}+4^x=4160\)

\(\Rightarrow4^x.4^3+4^x=4160\)

\(\Rightarrow4^x.\left(4^3+1\right)=4160\)

\(\Rightarrow4^x.65=4160\)

\(\Rightarrow4^x=4160:65\)

\(\Rightarrow4^x=64\)

\(\Rightarrow4^x=4^3\)

\(\Rightarrow x=3\)

\(4^{x+3}+4^x=4160\)

\(\left(4^x\cdot4^3\right)+4^x=4160\)

\(4^x\cdot\left(4^3+1\right)=4160\)

\(4^x\cdot\left(64+1\right)=4160\)

\(4^x\cdot65=4160\)

\(4^x=4160:65\)

\(4^x=64\)

\(\Rightarrow4^x=4^3\)

\(\Rightarrow x=3\)

Thưa toàn thể quý vị, chào mừng các bạn đến đây

\(4^{x+3}+4^x=4160\)

\(4^x\left(4^3+1\right)=4160\)

\(4^x.65=4160\)

\(4^x=4160:65\)

\(4^x=64\)

=> x = 3

b)\(2^{x-1}+5\cdot2^{x-2}=\frac{7}{32}\)

\(2^x:2+5\cdot2^x:2^2=\frac{7}{32}\)

\(2^x:2+2^x:\frac{4}{5}=\frac{7}{32}\)

\(2^x\cdot\left(\frac{1}{2}+\frac{5}{4}\right)=\frac{7}{32}\)

\(2^x\cdot\frac{7}{4}=\frac{7}{32}\)

\(2^x=\frac{7}{32}:\frac{7}{4}=\frac{1}{8}\)

\(2^x=\frac{2^0}{2^3}=2^{-3}\)

\(\Rightarrow x=-3\)

a) \(4^x+4^{x+3}=4160\)

\(\Rightarrow4^x+4^x.4^3=4160\)

\(\Rightarrow4^x.\left(1+4^3\right)=4160\)

\(\Rightarrow4^x.65=4160\)

\(\Rightarrow4^x=64\)

\(\Rightarrow4^x=4^4\)

\(\Rightarrow x=4\)

Vậy \(x=4\)

b) \(2^{x-1}+5.2^{x-2}=\frac{7}{32}\)

\(\Rightarrow2^x.\frac{1}{2}+5.2^x.\frac{1}{4}=\frac{7}{32}\)

\(\Rightarrow2^x.\left(\frac{1}{2}+5.\frac{1}{4}\right)=\frac{7}{32}\)

\(\Rightarrow2^x.\frac{7}{4}=\frac{7}{32}\)

\(\Rightarrow2^x=\frac{7}{32}:\frac{7}{4}\)

\(\Rightarrow2^x=\frac{1}{8}\)

\(\Rightarrow2^x=2^{-3}\)

\(\Rightarrow x=-3\)

Vậy \(x=-3\)

a)\(4^x+4^{x+3}=4160\)

\(4^x+4^x\cdot4^3=4160\)

\(4^x\left(1+4^3\right)=4160\)

\(4^x\cdot65=4160\)

\(4^x=4160:65=64\)

\(4^x=4^3\)

\(\Rightarrow x=3\)

=> 4^x[1 + 4³] = 4160

=> 4^x . 65 = 4160

=> 4^x = 64

=> x = 3

Ta có: 4\(^x\)+4\(^{x+3}\)=4160

\(\Rightarrow\)4\(^x\).(1+4\(^3\))=4160

\(\Rightarrow\)4\(^x\).65=4160

\(\Rightarrow\)4\(^x\)=64

\(\Rightarrow\)4\(^x\)=4\(^3\)\(\Rightarrow\)x=3

4\(^x\)+4\(^x\).64=4160

4\(^x\)(1+64)= 4160

4\(^x\)=4160:65=64

4\(^x\)=4\(^3\)

\(\Rightarrow\)x=3

\(4^x+4^{x+3}=4160\)

\(\Leftrightarrow4^x.\left(1+4^3\right)=4160\)

\(\Leftrightarrow4^x.65=4160\)

\(\Leftrightarrow4^x=4160:65=64\)

\(\Rightarrow x=3\)

ta có :

 4160 chia liên tục cho 4 được 9 lần 

mà 9 - 3 = 6 . vậy 2 lần x = 6

x = 6 : 2 =  3 

nhé !

dễ

Bạn tự suy nghĩ cách làm nhé !

\(4^x+4^{x+3}=4160\)

\(x=3\)

4^x(1+4³) = 4160

4^x = 64

x = 3