How do you solve #log_5(x+4)+log_5 8=log_5 64#?

2 Answers
Annie
Oct 27, 2016

#x=4#

Explanation:

#log_5 (x+4)+log_5 8# = #log_5 8(x+4)#

So #8(x+4)=64#

#x+4=8#
#x=4#

Have you understood the rules of indices?
100 x1000= 100,000
#10^2 #x#10^3=10^5#
So in terms of the index numbers
2+3=5
Or
#log_10 2+log_10 3=log_10 5#
Which is the same as
#log_10 (2 times 3) =log_10 5#

Aditya Banerjee.
Oct 29, 2016

Answer is #x=4#.

Explanation:

#log_5 (x+4)+log_5 8=log_5 64#
#:.log(x+4)+log8=log64#
#:.log(x+4)+log2^3=log 2^6#
#:.log(x+4)+3log2=6log2#
#:.log(x+4)=3log2#
#:.log(x+4)=log2^3#
#:.x+4=8#
#:.x=4#. (answer).

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