Question

considerando log base a 2 = 3 e log base a 3 = 5 calcule o valor de log base a 324.

Answer 1

Resposta:

26

Explicação passo a passo:

$\log _a2=3\\\\\log_a3=5\\\\\log _a324=?\\\\\\\\\log _a324=\log _a18^2\\\\=2\cdot \left(\log _a18\right)\\\\=2\cdot \left(\log _a\left(3^2\cdot 2\right)\right)\\\\=2\cdot \left(\log _a3^2+\log _a2\right)\\\\=2\cdot \left(2\cdot \log _a3+\log _a2\right)\\\\=2\cdot \left(2\cdot 5+3\right)\\\\=2\cdot \left(10+3\right)\\\\=2\cdot \left(13\right)\\\\=26$