What is the value of #x# in #log(5) = 2 - log(x)#?

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Answer 1 · 2015-12-16T23:59:13

#x=20#

Move the logarithms to the same side.

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

Now, use the following rule: #log_a(b)+log_a(c)=log_a(bc)#

#log(5x)=2#

Recall that #log(x)# is the shorter way of writing #log_10(x)#.

#log_10(5x)=2#

Exponentiate both sides to cancel the logarithm.

#10^(log_10(5x))=10^2#

#5x=100#

#x=20#