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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.

2 Answers2

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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.

Peter Foreman
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  • Minor note/addition: $\log_2(x)$ is apparently also the common interpretation of $\log(x)$ in computer science. To my understanding, what $\log(x)$ means w.r.t. its base is basically determined entirely by what is most commonly used in the relevant field/context. I personally hate that convention, but such is life. – PrincessEev Mar 12 '19 at 02:05
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For the solution you can use the LambertW function: $$x={{\rm e}^{-{\rm W} \left(1/20\,{{\rm e}^{1/2}}\right)+1/2}}$$

Dr. Sonnhard Graubner
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    The OP states that the question is intended for iGCSE students (14-17 years old) - I don't think this is the intended solution. – Peter Foreman Mar 11 '19 at 19:00
  • Thanks for the solution. @PeterForeman is right, this is too complicated for iGCSE students. The answer was to draw the function f(x) = log (x) and then to draw the line g(x) = (10-x)/20. –  Mar 11 '19 at 19:59
  • Acquiring more knowledge does not harm. – cgiovanardi Mar 12 '19 at 01:01