Question

Tìm x biết:

1.  5^{2x - 3}   - 2 . 5² = 5² . 3

2. 41 - 2^x+1 = 9

3. 65 - 4^x+2 = 2014⁰ 

Answer 1

1: =>\(5^{2x-3}=5^2\cdot3+5^2\cdot2=5^2\cdot5=5^3\)

=>2x-3=3

=>2x=6

=>x=3

2: \(41-2^{x+1}=9\)

=>\(2^{x+1}=32\)

=>x+1=5

=>x=4

3: =>\(4^{x+2}=65-1=64\)

=>x+2=3

=>x=1

Answer 2

\(5^{2x-3}-2.5^2=5^2.3\\ 5^{2x-3}=5^2.3+5^2.2\\ 5^{2x-3}=5^2.\left(3+2\right)\\ 5^{2x-3}=5^2.5\\ 5^{2x-3}=5^3\\ \Rightarrow2x-3=3\\ 2x=3+3\\ 2x=6\\ x=\dfrac{6}{2}\\ Vậy:x=3\)

Answer 3

\(41-2^{x+1}=9\\ 2^{x+1}=41-9\\ 2^{x+1}=32=2^5\\ \Rightarrow x+1=5\\ \Leftrightarrow x=5-1=4\\ ---\\ 65-4^{x+2}=2014^0\\ 65-4^{x+2}=1\\ 4^{x+2}=65-1\\ 4^{x+2}=64=4^3\\ \Rightarrow x+2=3\\ Vậy:x=1\)