Bagaimana Anda menyelesaikan log (2 + x) -log (x-5) = log 2?

Menjawab:

# x = 12 #

Penjelasan:

Menulis ulang sebagai ekspresi logaritmik tunggal

catatan: #log (a) - log (b) = log (a / b) #

#log (2 + x) - log (x-5) = log2 #

#log ((2 + x) / (x-5)) = log 2 #

# 10 ^ log ((2 + x) / (x-5)) = 10 ^ (log2) #

# (2 + x) / (x-5) = 2 #

# (2 + x) / (x-5) * warna (merah) ((x-5)) = 2 * warna (merah) ((x-5)) #

# (2 + x) / batal (x-5) * batal ((x-5)) = 2 (x-5) #

# 2 + x "" "= 2x-10 #

# + 10 - x = -x + 10 #

===============

#color (red) (12 "" "= x) #

Periksa:

#log (12 + 2) - log (12-5) = log 2 # ?

#log (14) - log (7) #

#log (14/7) #

#log 2 = log 2 #

Ya, jawabannya # x = 12 #