Giải phương trình:
a) $2^{2x-1}=32$.
b) ${\left(\frac{2}{3}\right)}^{4x}={\left(\frac{3}{2}\right)}^{2x-6}$
c) ${\sqrt{2}}^{x^2+2x+3}=8^x$
d) $3^{x+5}=8$
e) $e^{x^2}=\sqrt{3}$
f) $4^{2x+5}=2^{2-x}$
g) $10^{x+2}=25$
h) $3^x.5^{x-1}=7$

(AI giải đề cho tôi)
Bài 5 – Giải các phương trình mũ, lôgarit:

a) $2^{2x-1}=32=2^5\Rightarrow 2x-1=5\Rightarrow x=3$.

b) ${\left(\frac{2}{3}\right)}^{4x}={\left(\frac{3}{2}\right)}^{2x-6}={\left(\frac{2}{3}\right)}^{6-2x}$. Vì cơ số $\frac{2}{3}\ne 1$ nên $4x=6-2x\Rightarrow 6x=6\Rightarrow x=1$.

c) ${\sqrt{2}}^{x^2+2x+3}=8^x\iff 2^{\frac{x^2+2x+3}{2}}=2^{3x}\Rightarrow \frac{x^2+2x+3}{2}=3x\Rightarrow x^2-4x+3=0\Rightarrow x=1$ hoặc $x=3$.

d) $3^{x+5}=8\Rightarrow x+5={\log }_{3}8=3{\log }_{3}2\Rightarrow x=3{\log }_{3}2-5$.

e) $e^{x^2}=\sqrt{3}\Rightarrow x^2=\ln \sqrt{3}=\frac{1}{2}\ln 3\Rightarrow x=\pm \sqrt{\frac{\ln 3}{2}}$.

f) $4^{2x+5}=2^{2-x}\iff 2^{4x+10}=2^{2-x}\Rightarrow 4x+10=2-x\Rightarrow 5x=-8\Rightarrow x=-\frac{8}{5}$.

g) $10^{x+2}=25\Rightarrow x+2=\log 25=2\log 5\Rightarrow x=2\log 5-2=\log \frac{25}{100}=\log \frac{1}{4}$.

h) $3^x\cdot 5^{x-1}=7\iff \frac{3^x\cdot 5^x}{5}=7\iff 15^x=35\Rightarrow x={\log }_{15}35$.

Kiểm tra lại: a) $2^5=32$ đúng; b) $x=1$: $(2/3{)}^4=(3/2{)}^{-4}$ đúng; c) $x=1$: $2^{6/2}=2^3=8$ đúng, $x=3$: $2^{18/2}=2^9=8^3$ đúng; f) $x=-8/5$: $4^{-8/5+5}=4^{17/5}=2^{34/5}$, $2^{2+8/5}=2^{18/5}$... kiểm tra lại: $2x+5=-16/5+5=9/5$, nên $4^{9/5}=2^{18/5}$ và $2^{2-(-8/5)}=2^{18/5}$ đúng.