Đáp án:

$a)x=5\\ b) \left[\begin{array}{l}x=0 \\ x=\pm 1\end{array} \right.\\ c)x=2\\ d)\left[\begin{array}{l} x=5\\ x=6 \\ x=4 \end{array} \right.\\ e)x=5\\ g)x=3\\ h) \left[\begin{array}{l}x=0 \\ x=1\end{array} \right.$

Giải thích các bước giải:

$a)2^x.4=128\\ \Leftrightarrow 2^x=\dfrac{128}{4}\\ \Leftrightarrow 2^x=32\\ \Leftrightarrow 2^x=2^5\\ \Leftrightarrow x=5\\ b)x^{15}=x\\ \Leftrightarrow x^{15}-x=0\\ \Leftrightarrow x(x^{14}-1)=0\\ \Leftrightarrow  \left[\begin{array}{l}x=0 \\ x^{14}-1=0 \end{array} \right.\\ \Leftrightarrow  \left[\begin{array}{l}x=0 \\ x^{14}=1 \end{array} \right.\\ \Leftrightarrow  \left[\begin{array}{l}x=0 \\ x=\pm 1\end{array} \right.\\ c)(2x+1)^3=125\\ \Leftrightarrow (2x+1)^3=5^3\\ \Leftrightarrow 2x+1=5\\ \Leftrightarrow 2x=4\\ \Leftrightarrow x=2\\ d)(x-5)^4=(x-5)^6\\ \Leftrightarrow (x-5)^4-(x-5)^6=0\\ \Leftrightarrow (x-5)^4\left[1-(x-5)^2\right]=0\\ \Leftrightarrow  \left[\begin{array}{l} (x-5)^4=0\\ 1-(x-5)^2=0\end{array} \right.\\ \Leftrightarrow  \left[\begin{array}{l} x-5=0\\ (x-5)^2=1\end{array} \right.\\ \Leftrightarrow  \left[\begin{array}{l} x=5\\ x-5=1 \\ x-5=-1 \end{array} \right.\\ \Leftrightarrow  \left[\begin{array}{l} x=5\\ x=6 \\ x=4 \end{array} \right.\\ e)2^x-15=17\\ \Leftrightarrow 2^x=17+15\\ \Leftrightarrow 2^x=32\\ \Leftrightarrow 2^x=2^5\\ \Leftrightarrow x=5\\ g)(7x-11)^3=2^5.5^2+200\\ \Leftrightarrow (7x-11)^3=32.25+200\\ \Leftrightarrow (7x-11)^3=800+200\\ \Leftrightarrow (7x-11)^3=1000\\ \Leftrightarrow (7x-11)^3=10^3\\ \Leftrightarrow 7x-11=10\\ \Leftrightarrow 7x=10+11\\ \Leftrightarrow 7x=21\\ \Leftrightarrow x=3\\ h)x^{10}=x\\ \Leftrightarrow x^{10}-x=0\\ \Leftrightarrow x(x^{9}-1)=0\\ \Leftrightarrow  \left[\begin{array}{l}x=0 \\ x^{9}-1=0 \end{array} \right.\\ \Leftrightarrow  \left[\begin{array}{l}x=0 \\ x^{9}=1\end{array} \right.\\ \Leftrightarrow  \left[\begin{array}{l}x=0 \\ x=1\end{array} \right.$

Đáp án:

$\\$

`a,`

`2^x ×4 = 128`

`↔ 2^x = 128 ÷ 4`

`↔ 2^x = 32`

`↔ 2^x = 2^5`

`↔x=5`

Vậy `x=5`

$\\$

`b,`

`x^{15} = x`

`↔ x^{15} - x = 0`

`↔ x (x^{14} - 1) = 0`

Trường hợp 1 :

`↔x=`0

Trường hợp 2 :

`↔x^{14}-1=0`

`↔x^{14}=0+1`

`↔x^{14}=1`

`↔` \(\left[ \begin{array}{l}x^{14}=1^{14}\\x^{14}=(-1)^{14}\end{array} \right.\) 

`↔` \(\left[ \begin{array}{l}x=1\\x=-1\end{array} \right.\) 

Vậy `x=0,x=1,x=-1`

$\\$

`c,`

`(2x+1)^3 = 125`

`↔ (2x+1)^3=5^3`

`↔2x+1=5`

`↔2x=5-1`

`↔2x=4`

`↔x=4÷2`

`↔x=2`

Vậy `x=2`

$\\$

`d,`

`(x-5)^4 = (x-5)^6`

`↔ (x-5)^4 - (x-5)^6 = 0`

`↔ (x-5)^4 - (x-5)^4 × (x-5)^2 = 0`

`↔ [1 - (x-5)^2] (x-5)^4 =0`

Trường hợp 1 :

`↔ 1 - (x-5)^2=0`

`↔(x-5)^2=1-0`

`↔(x-5)^2=1`

`↔` \(\left[ \begin{array}{l}(x-5)^2=1^2\\(x-5)^2=(-1)^2\end{array} \right.\) 

`↔` \(\left[ \begin{array}{l}x-5=1\\x-5=-1\end{array} \right.\) 

`↔` \(\left[ \begin{array}{l}x=1+5\\x=-1+5\end{array} \right.\) 

`↔` \(\left[ \begin{array}{l}x=6\\x=4\end{array} \right.\) 

Trường hợp 2 :

`↔ (x-5)^4=0`

`↔x-5=0`

`↔x=0+5`

`↔x=5`

Vậy `x=6,x=4,x=5`

$\\$

`e,`

`2^x - 15 = 17`

`↔ 2^x=17+15`

`↔2^x=32`

`↔ 2^x = 2^5`

`↔x=5`

Vậy `x=5`

$\\$

`g,`

`(7x - 11)^3 =2^5 × 5^2 + 200`

`↔ (7x-11)^3=32 × 25 + 200`

`↔ (7x-11)^3=800 + 200`

`↔ (7x-11)^3=1000`

`↔ (7x-11)^3=10^3`

`↔7x-11=10`

`↔7x=10+11`

`↔7x=21`

`↔x=21÷7`

`↔x=3`

Vậy `x=3`

$\\$

`h,`

`x^{10}=x`

`↔x^{10}-x=0`

`↔x (x^9-1)=0`

Trường hợp 1 :

`↔x=0`

Trường hợp 2 :

`↔x^9-1=0`

`↔x^9=0+1`

`↔x^9=1`

`↔x^9=1^9`

`↔x=1`

Vậy `x=0,x=1`