How do you solve #Log( 4x - 3) = 2#?

1 Answer
Alan P.
Dec 12, 2016

#color(green)(x=103/4)#

Explanation:

It is important to remember the basic relation:

#color(red)("~~~~~~~~~~~~~~~~~~~~~~~~~~~")#
#color(red)("| ")color(blue)(log_b a =c)" means "color(blue)(b^c=a)color(red)(" |")#
#color(red)("~~~~~~~~~~~~~~~~~~~~~~~~~~~")#

(also remember that the default base for #log# is #10#)

Therefore
#color(white)("XXX")log(4x-3)=2 hArr log_10 (4x-3)=2#
means
#color(white)("XXX")10^2=4x-3#

#rarr 4x-3=100#

#rarr 4x=103#

#rarr x=103/4#

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