Question

Tìm x biết:

a) 7^x+2 + 2.7^x-1= 345

b) 2^x+2 - 2^x= 96

Answer 1

a.

\(7^{x+2}+2\times7^{x-1}=345\)

\(7^x\times7^2+2\times7^x\div7=345\)

\(7^x\times\left(7^2+\frac{2}{7}\right)=345\)

\(7^x\times\frac{345}{7}=345\)

\(7^x=345\div\frac{345}{7}\)

\(7^x=345\times\frac{7}{345}\)

\(7^x=7\)

\(x=1\)

b.

\(2^{x+2}-2^x=96\)

\(2^x\times\left(2^2-1\right)=96\)

\(2^x\times3=96\)

\(2^x=\frac{96}{3}\)

\(2^x=32\)

\(2^x=2^5\)

\(x=5\)

Answer 2

\(a,7^{x+2}+2.7^{x-1}=345\Rightarrow7^x.49+\frac{2}{7}.7^x=345\Rightarrow7^x\left(49+\frac{2}{7}\right)=345\Rightarrow7^x.\frac{345}{7}=345\Rightarrow7^x=345:\frac{345}{7}=7^1\Rightarrow x=1\)

\(b,2^{x+2}-2^x=96\Rightarrow2^x.4-2^x=96\Rightarrow2^x\left(4-1\right)=96\Rightarrow2^x.3=96\Rightarrow2^x=96:3=32\Rightarrow2^x=2^5\Rightarrow x=5\)