How do you solve #1+ 3\log _ { 2} ( x + 5) = 7#?

1 Answer
Mia
Nov 27, 2016

#x=-1#

Explanation:

Solving the equation is based on a fundamental property ,the
#" "#
reciprocal of a logarithm.
#" "#
Property:
#" "#
If #color(blue)(" "log_a x = b " "then" "x=b^a)#
#" "#
#1+3log_2(x+5) = 7#
#" "#
#rArr3log_2(x+5)=7-1#
#" "#
#rArr3log_2(x+5)=6#
#" "#
#rArrlog_2(x+5)=6/3#
#" "#
#rArrlog_2(x+5)=2#
#" "#
#rArr color(blue)(x+5=2^2)#
#" "#
#rArrx+5=4#
#" "#
#rArrx=4-5#
#" "#
#rArrx=-1#

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