Question

B) log(2x+10) - log(x+1)= log 4
C) log6 (x-5) + log6 (x+5)= log6 11

No gabarito diz que a B= S{3} C={6}

Answer 1

B) log(2x + 10) - log(x + 1) = log 4
$\log(2(x+5))-\log(x+1)=log(2^2)\\\\ \log(2)+\log(x+5)-\log(x+1)=2log(2)\\\\ \log(x+5)-\log(x+1)=\log(2)\\\\ \log(x+5)=\log(2)+\log(x+1)\\\\ \log(x+5)=\log(2(x+1))\\\\ \log(2(x+1))-\log(x+5)=0\\\\ \log(\frac{2(x+1)}{x+5} )=0\\\\ 10^0 = \frac{2(x+1)}{x+5}\\\\ \frac{2(x+1)}{x+5} = 1 \\\\ 2(x+1) = x+5\\\\ 2x + 2 = x + 5\\\\ \boxed{x = 3}$

S={3}

C) log6 (x-5) + log6 (x+5)= log6 11
$\log_6(x-5) + \log_6(x+5) = \log_6(11)\\\\ \log_6((x-5)\times(x+5)) = \log_6(11)\\\\ \log_6(x^2-25) = \log_6(11)\\\\ \log_6( \frac{x^2-25}{11}) = 0\\\\ 6^0=\frac{x^2-25}{11}\\\\ \frac{x^2-25}{11} = 1\\\\ x^2-25 = 11\\\\ x^2 = 36\\\\ \sqrt{x^2} = \sqrt{36}\\\\ \boxed{x = 6}$

S={6}