[tex]3^{2x-3} .9^{x-1} =9^{x+\frac{1}{2} } \\\\3^{2x-3} .(3^{2}) ^{x-1} =9^{x}.9^{\frac{1}{2}} \\\\3^{2x-3} .3^{2x-2} =(3^{2} )^{x}.\sqrt{9} \\\\3^{2x-3+2x-2} =3^{2x}.3 \\\\3^{4x-5} =3^{2x+1} \\\\4x-5=2x+1\\\\4x-2x=1+5\\\\2x=6\\\\x=\frac{6}{2} \\\\\bold{x=3}[/tex]
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Resposta:
x = 3
Explicação passo a passo:
[tex]3^{2x-3} .9^{x-1} =9^{x+\frac{1}{2} } \\\\3^{2x-3} .(3^{2}) ^{x-1} =9^{x}.9^{\frac{1}{2}} \\\\3^{2x-3} .3^{2x-2} =(3^{2} )^{x}.\sqrt{9} \\\\3^{2x-3+2x-2} =3^{2x}.3 \\\\3^{4x-5} =3^{2x+1} \\\\4x-5=2x+1\\\\4x-2x=1+5\\\\2x=6\\\\x=\frac{6}{2} \\\\\bold{x=3}[/tex]