a)
[tex]2^{3x-1}=32\\\\2^{3x-1}=2^5\\\\3x-1=5\\\\3x=5+1\\\\3x=6 \ \ /:3\\\\\huge\boxed{x=2}[/tex]
b)
[tex]5^{2x+5}=125\\\\5^{2x+5}=5^3\\\\2x+5=3\\\\2x=3-5\\\\2x=-2 \ \ /:2\\\\\huge\boxed{x=-1}[/tex]
c)
[tex]121^{\frac{1}{2}-x}=11^{x-x^2}\\\\(11^2)^{\frac{1}{2}-x}=11^{x-x^2}\\\\11^{1-2x}=11^{x-x^2}\\\\1-2x=x-x^2\\\\1-2x-x+x^2=0\\\\x^2-3x+1=0\\\\\Delta=(-3)^2-4\cdot1\cdot1=9-4=5\\\\\sqrt{\Delta}=\sqrt5\\\\x_1=\frac{-(-3)-\sqrt5}{2}=\boxed{\frac{3-\sqrt5}{2}}\\\\x_2=\frac{-(-3)+\sqrt5}{2}=\boxed{\frac{3+\sqrt5}{2}}[/tex]
d)
[tex]3^{x+5}=\frac{1}{3}\\\\3^{x+5}=3^{-1}\\\\x+5=-1\\\\x=-1-5\\\\\huge\boxed{x=-6}[/tex]
