Whats the answer to log(x-1) = -1 ?

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Answer 1 · 2018-06-21T21:35:48

#x=1.1#

Given that
#\log(x-1)=-1#

Taking Antilog on both the sides

#\text{Antilog}(\log(x-1))=\text{Antilog}(-1)#

#x-1=10^{-1}#

#x-1=\frac{1}{10}#

#x=1+\frac{1}{10}#

#x=\frac{11}{10}#

#x=1.1#

Answer 2 · 2018-06-21T23:27:36

#x=11/10#

The key realization is that if we have a logarithm of the form

#log_ba=x#, that this is equal to

#b^x=a#

NOTE: If there's no base on the logarithm, it is implicitly base-10.

This means we can rewrite our logarithm as

#10^(-1)=x-1#

Which simplifies to

#1/10=x-1#

Adding #1# to both sides, we get

#x=11/10#

Hope this helps!