GCSE logarithmic problem - don't know base

Question

There's a question in my iGCSE textbook that I don't know how to answer. I HAVE TRIED TO ANSWER IT! The question is: $$log(x)=\frac{10-x}{20}$$ I don't know what the base for the $log()$ is. Putting this question into Wolfram Alpha or other equation solvers doesn't work.

Please help! Thanks.

Answer 1

It is either the natural logarithm and hence has base $e$ or the base $10$ logarithm. Either logarithms can be represented by the symbol $\log{(x)}$ and it cannot be determined without other contextual information.

Although, it is standard in GCSE problems that $\ln{(x)}$ means the natural logarithm (base $e$) and $\log{(x)}$ means the base $10$ logarithm.

Although, the solution to this equation can only be found by using numerical methods (a calculator) so I do not think it would be printed as written for iGCSE students.

Answer 2

For the solution you can use the LambertW function: $$x={{\rm e}^{-{\rm W} \left(1/20\,{{\rm e}^{1/2}}\right)+1/2}}$$