Question

Log5 625 + log 100 + log3 27

Answer 1

log_{5}(625)  \\ {5}^{x}  = 625 \\ 5 {}^{x} =  {5}^{4} \\  x = 4  

log_{5}(625)  = 4

log_{10}(100)  =  \\ 10 {}^{x} = 100 \\  {10}^{x} = 10 {}^{2} \\ x = 2    

log(100) = 2  

log_{3}(27) =  \\  {3}^{x} = 27 \\  {3}^{x} = 3 {}^{3} \\ x = 3    

log_{3}(27)  = 3

Substituindo

log_{5}(625)  +  log(100) +  log_{3}(27)   =  \\ 4 + 2 - 3 =  \\ 3