Đáp án:

f) $x = -\dfrac12$

g) $x = \dfrac75$

h) Phương trình vô nghiệm

Giải thích các bước giải:

$\begin{array}{l}f)\quad 18^{\displaystyle{2x}}.2^{\displaystyle{-2x}}.3^{\displaystyle{x+1}}=3^{\displaystyle{x-1}} \\ \Leftrightarrow (3^2.2)^{\displaystyle{2x}}.2^{\displaystyle{-2x}}.3^{\displaystyle{x+1}}=3^{\displaystyle{x-1}} \\ \Leftrightarrow 3^{\displaystyle{4x}}.3^{\displaystyle{x+1}}=3^{\displaystyle{x-1}} \\ \Leftrightarrow 3^{\displaystyle{5x+1}}=3^{\displaystyle{x-1}} \\ \Leftrightarrow 5x + 1 = x - 1\\ \Leftrightarrow 4x = -2\\ \Leftrightarrow x = -\dfrac12\\ Vậy\,\,x = -\dfrac12\\ g)\quad 5^{\displaystyle{\vert4x - 6\vert}}=25^{\displaystyle{3x - 4}}\\ \Leftrightarrow 5^{\displaystyle{\vert4x - 6\vert}}=(5^2)^{\displaystyle{3x - 4}}\\ \Leftrightarrow 5^{\displaystyle{\vert4x - 6\vert}}=5^{\displaystyle{6x - 8}}\\ \Leftrightarrow \vert4x - 6\vert = 6x - 8\\ \Leftrightarrow \left[\begin{array}{l}4x - 6 = 6x - 8\qquad \left(x \geq \dfrac32\right)\\4x- 6 = 8 - 6x\qquad \left(x < \dfrac32\right)\end{array}\right.\\ \Leftrightarrow \left[\begin{array}{l}x = 1\qquad (loại)\qquad \left(x \geq \dfrac32\right)\\x = \dfrac{7}{5}\quad (nhận)\qquad \left(x < \dfrac32\right)\end{array}\right.\\ Vậy\,\,x = \dfrac{7}{5}\\ h)\quad \left(\dfrac53\right)^{\displaystyle{x+1}}\cdot\left(\dfrac{9}{25}\right)^{\displaystyle{x^2 + 2x - 1}}= \left(\dfrac53\right)^9\\ \Leftrightarrow \left(\dfrac53\right)^{\displaystyle{x+1}}\cdot\left[\left(\dfrac{3}{5}\right)^2\right]^{\displaystyle{x^2 + 2x - 1}}= \left(\dfrac53\right)^9\\ \Leftrightarrow \left(\dfrac53\right)^{\displaystyle{x+1}}\cdot\left(\dfrac{3}{5}\right)^{\displaystyle{2x^2 + 4x - 2}}= \left(\dfrac53\right)^9\\ \Leftrightarrow \left(\dfrac53\right)^{\displaystyle{x+1}}\cdot\left(\dfrac{5}{3}\right)^{\displaystyle{-2x^2 - 4x + 2}}= \left(\dfrac53\right)^9\\ \Leftrightarrow \left(\dfrac{5}{3}\right)^{\displaystyle{-2x^2 - 3x + 3}}= \left(\dfrac53\right)^9\\ \Leftrightarrow -2x^2 - 3x + 3 = 9\\ \Leftrightarrow 2x^2 + 3x + 6 = 0\quad \text{(vô nghiệm)}\\ \text{Vậy phương trình đã cho vô nghiệm} \end{array}$