Question

sendo log a=20 e log a 5= 30 , cauculem o valor de log a 100

Answer 1

$\log_{a}(2)=20;\qquad\log_a(5)=30;\qquad\log_a(100)=\,\,?\\\\\\\log_a(100)=\log_a(2^2\cdot5^2)\longrightarrow\log_a(100)=\log_a(2^2)+\log_a(5^2)\longrightarrow\\\\\log_a(100)=2\log_a(2)+2\log_a(5)\longrightarrow\log_a(100)=2(\log_a(2)+\log_a(5))\longrightarrow\\\\\log_a(100)=2(20+30)\longrightarrow\boxed{\boxed{\log_a(100)=100}}$