What is x if #-log(5x) = -3#?

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Answer 1 · 2015-10-22T22:44:07

#-log(5x) = -3# if and only of

#log(5x) = 3#

And that is true if and only if #5x = b^3# for whatever base you intend by #log#.

Traditionally #log# without a subscript meant the Common Logarithm which is the base 10 log, so we would have

#5x=10^3 = 1000#, so #x=1000/5 = 200#

Many people now use #log# to mean the Natural Log (log base #e#)

In that case we get #5x=e^3# so #x = e^3/5#
(Which can be found without a table or a calculator, but it's a bit tedious.)