How do you solve #log(x-2)-log(2x-3)=log2#?

1 Answer
Mar 24, 2018

In the explanation. ..

Explanation:

Use the property of condensation of logarithmic function
Given,
#log (x-2)-log (2x-3)=log (2)#
# or, log ((x-2)/(2x-3)) = log (2)#

# or, 10^(log ((x-2)/(2x-3))=10^(log (2))#
# or, (x-2)/(2x-3)=2#
# or, (x-2)=2 (2x-3)#
# or, (x-2)=4x-6#
# or, -2+6=4x-x#
# or, 4=3x#
#:.x=4/3#