Resposta :
Estou enferrujado em log, mas vamos ver se acerto ...
[tex]\log x = 3 + (log3 -log2) - 2* log5[/tex]
[tex]\log x + 2 \log5 = ( \log3-\log2)+3[/tex]
[tex]\log x +\log 5^2 = \log (3/2) +3[/tex]
[tex]\log25x=\log(3/2) +3[/tex]
[tex]\log( \frac{25x}{ \frac{3}{2}}})=3[/tex]
[tex]\log( \frac{50x}{3})=3[/tex]
[tex]10^3 = \frac{50x}{3} [/tex]
[tex]1000= \frac{50x}{3} [/tex]
[tex]3000=50x[/tex]
[tex] \frac{3000}{50} =x[/tex]
x = 60
[tex]\log x = 3 + (log3 -log2) - 2* log5[/tex]
[tex]\log x + 2 \log5 = ( \log3-\log2)+3[/tex]
[tex]\log x +\log 5^2 = \log (3/2) +3[/tex]
[tex]\log25x=\log(3/2) +3[/tex]
[tex]\log( \frac{25x}{ \frac{3}{2}}})=3[/tex]
[tex]\log( \frac{50x}{3})=3[/tex]
[tex]10^3 = \frac{50x}{3} [/tex]
[tex]1000= \frac{50x}{3} [/tex]
[tex]3000=50x[/tex]
[tex] \frac{3000}{50} =x[/tex]
x = 60
[tex]log_{x} a + log_{x} b <=> log_{x} (a*b)[/tex]
[tex]log_{x} a - log_{x} b <=> log_{x} (a/b)[/tex]
[tex]log_{x}(a^{n}) = n * log_{x}a[/tex]
_____________________________
[tex]logx = 3 + (log3 - log2) - 2*log5[/tex]
[tex]logx = 3 + log3 - log2 - log5^{2}[/tex]
[tex]logx = log10^{3} + log3 - log2 - log25[/tex]
[tex]logx = log(10^{3}*3 / [2*25])[/tex]
[tex]logx = log(3000/50)[/tex]
[tex]logx = log60[/tex]
[tex]x = 60[/tex]
[tex]log_{x} a - log_{x} b <=> log_{x} (a/b)[/tex]
[tex]log_{x}(a^{n}) = n * log_{x}a[/tex]
_____________________________
[tex]logx = 3 + (log3 - log2) - 2*log5[/tex]
[tex]logx = 3 + log3 - log2 - log5^{2}[/tex]
[tex]logx = log10^{3} + log3 - log2 - log25[/tex]
[tex]logx = log(10^{3}*3 / [2*25])[/tex]
[tex]logx = log(3000/50)[/tex]
[tex]logx = log60[/tex]
[tex]x = 60[/tex]