Bài 2:

a) \(2^n-64=0\)

\(2^n=64\)

\(2^n=2^6\)

\(n=6\)

b) \(5.3^{n-3}-405=0\)

\(5.3^{n-3}=405\)

\(3^{n-3}=405:5\)

\(3^{n-3}=81\)

\(n-3=4\)

\(n=4+3\)

\(n=7\)

c) \(4^n.8=2^{15}\)

\(\left(2^2\right)^n.2^3=2^{15}\)

\(2^{2n}.2^3=2^{15}\)

\(2^{2n+3}=2^{15}\)

\(2n+3=15\)

\(2n=15-3\)

\(2n=12\)

\(n=12:2\)

\(n=6\)

d) \(3.2^{n+1}+2^{n+2}=160\)

\(2^{n+1}.\left(3+2\right)=160\)

\(2^{n+1}.5=160\)

\(2^{n+1}=160:5\)

\(2^{n+1}=32\)

\(2^{n+1}=2^5\)

\(n+1=5\)

\(n=5-1\)

\(n=4\)

Bài 1

a) \(2^{11}.64=2^{11}.2^6=2^{17}\)

Do \(16< 17\Rightarrow2^{16}< 2^{17}\)

Vậy \(2^{16}< 2^{11}.64\)

b) Do \(18>17\Rightarrow9^{18}>9^{17}\)   (1)

\(9^{18}=\left(3^2\right)^{18}=3^{36}\)

Do \(36< 37\Rightarrow3^{36}< 3^{37}\)

\(\Rightarrow9^{18}< 3^{37}\)  (2)

Từ (1) và (2) \(\Rightarrow9^{17}< 3^{37}\)

c) \(2^{333}=\left(2^3\right)^{111}=8^{111}\)

\(3^{222}=\left(3^2\right)^{111}=9^{111}\)

Do \(8< 9\Rightarrow8^{111}< 9^{111}\)

Vậy \(2^{333}< 3^{222}\)

d) \(3^{50}=\left(3^2\right)^{25}=9^{25}\)

Do \(9< 11\Rightarrow9^{25}< 11^{25}\)

Vậy \(3^{50}< 11^{25}\)

e) \(37< 38\Rightarrow3^{37}< 3^{38}\) (1)

Lại có: \(3^{38}=3^{2.19}=\left(3^2\right)^{19}=9^{19}\)

Do \(9< 10\Rightarrow9^{19}< 10^{19}\)

\(\Rightarrow3^{38}< 10^{19}\) (2)

Từ (1) và (2) \(\Rightarrow3^{37}< 10^{19}\)

f) Do \(17>16\Rightarrow17^{14}>16^{14}\)   (1)

Do \(32>31\Rightarrow32^{11}>31^{11}\)   (2)

Lại có:

\(16^{14}=\left(2^4\right)^{14}=2^{56}\)

\(32^{11}=\left(2^5\right)^{11}=2^{55}\)

Do \(56>55\Rightarrow2^{56}>2^{55}\)

\(\Rightarrow16^{14}>32^{11}\)   (3)

Từ (1), (2) và (3) \(\Rightarrow17^{14}>31^{11}\)

Mình mắc câu này 

= \(x^2+5x+6-\left(x^2+3x-10\right)\)

= \(x^2+5x+6-x^2-3x+10\)

= \(2x+16\)

= \(2\left(x+8\right)\)

\(\left(x+2\right)\left(x+3\right)-\left(x-2\right)\left(x+5\right)\)

\(=x^2+5x+6-\left(x^2+3x-10\right)\)

\(=2x+16\)

   (x+2).(x+3)-(x-2).(x+5)

=2x+16

Giải:

Ta có: \(3\left(x-1\right)=2\left(y-2\right)\Rightarrow\frac{x-1}{2}=\frac{y-2}{3}\)

\(4\left(y-2\right)=3\left(z-3\right)\Rightarrow\frac{y-2}{3}=\frac{z-3}{4}\)

\(\Rightarrow\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}\)

Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}=\frac{2x-2}{4}=\frac{3y-6}{9}=\frac{z-3}{4}=\frac{2x-2+3y-6+z-3}{4+9+4}=\frac{\left(2x+3y+z\right)-\left(2+6+3\right)}{17}\)

\(=\frac{50-11}{17}=\frac{39}{17}\)

+) \(\frac{x-1}{2}=\frac{39}{17}\Rightarrow x-1=\frac{78}{17}\Rightarrow x=\frac{95}{17}\)

+) \(\frac{y-2}{3}=\frac{39}{17}\Rightarrow y-2=\frac{117}{17}\Rightarrow y=\frac{151}{17}\)

+) \(\frac{z-3}{4}=\frac{39}{17}\Rightarrow z-3=\frac{156}{17}\Rightarrow z=\frac{207}{17}\)

Vậy bộ số \(\left(x;y;z\right)\) là \(\left(\frac{95}{17};\frac{151}{17};\frac{207}{17}\right)\)