[tex]log_{x} 2 = a[/tex]
[tex]log_{x} 3 = b[/tex]
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[tex]log_{x}(3 \sqrt{12}) = log_{x} (3 \sqrt{3*4}) [/tex]
[tex]log_{x}(3 \sqrt{12}) = log_{x} [3( \sqrt{3} * \sqrt{4})][/tex]
[tex]log_{x}(3 \sqrt{12})=log_{x} [3( \sqrt{3} *2)][/tex]
[tex]log_{x}(3 \sqrt{12})=log_{x}(3*2*\sqrt{3})[/tex]
[tex]log_{x}(3 \sqrt{12})=log_{x}(3*2*3^{1/2})[/tex]
[tex]log_{x}(3 \sqrt{12})= log_{x}3+log_{x}2 + log_{x} 3^{1/2}[/tex]
[tex]log_{x}(3 \sqrt{12})= b + a + (1/2)*log_{x}3[/tex]
[tex]log_{x}(3 \sqrt{12})= b + a + (1/2)*b[/tex]
[tex]log_{x}(3 \sqrt{12})= b + a + (b/2)[/tex]
Multiplicando todos os membros por 2:
[tex]2*log_{x}(3 \sqrt{12})=2*b+2*a+2*(b/2)[/tex]
[tex]2*log_{x}(3 \sqrt{12})=2b + 2a + b[/tex]
[tex]2*log_{x}(3 \sqrt{12})=2a + 3b[/tex]
[tex]log_{x}(3 \sqrt{12})=(2a+3b)/2[/tex]
