Question

Answer 1

Bài 12:

a: \(A=1+2+2^2+\cdots+2^{2007}\)

=>\(2A=2+2^2+2^3+\cdots+2^{2008}\)

b: 2A-A=\(2+2^2+2^3+\cdots+2^{2008}-1-2-2^2-\cdots-2^{2007}\)

=>\(A=2^{2008}-1\)

Bài 10:

c: \(2x-2^6=6\)

=>2x-64=6

=>2x=64+6=70

=>x=35

d: \(64\cdot4^{x}=4^5\)

=>\(4^{x}\cdot4^3=4^5\)

=>x+3=5

=>x=2

e: \(27\cdot3^{x}=243\)

=>\(3^{x}=\frac{243}{27}=9=3^2\)

=>x=2

g: \(49\cdot7^{x}=2401\)

=>\(7^{x}=\frac{2401}{49}=49=7^2\)

=>x=2

h: \(3^{x}=81\)

=>\(3^{x}=3^4\)

=>x=4

k: \(3^4\cdot3^{x}=3^7\)

=>\(3^{x+4}=3^7\)

=>x+4=7

=>x=3

n: \(3^{x}+25=26\cdot2^2+2\cdot3^0\)

=>\(3^{x}+25=26\cdot4+2=104+2=106\)

=>\(3^{x}=81=3^4\)

=>x=4