Updated: Oct 21, I found myself asking this question after studying logarithms in school. Logs was always one of the less popular, less well-known topics at GCSE. So when people saw they were in the A-Level syllabus, many said "I hate logs" immediately after looking at the list of log rules. But, logs are very similar to indices.
And after solving several problems, I noticed - all numbers that are put into the log function are always positive. But why is this? Below, I try to summarise how I figured it out.
As I said earlier, we can think of logs like indices. The base of the log is the base of the exponent function. Observe the result on the left. Well, we know that 0 raised to any power is still 0. Now let's imagine the base is 1 i. Again, just like last time, 1 raised to any power is just 1. So again, no matter what value x takes, y cannot be determined.
This means the base cannot be 1. But then I realised - log base 1 of 1 can, in fact, be any number. As we established earlier, 1 raised to any power gives 1. So, technically y can take ANY number.
Because the logarithm is the inverse function of the exponential operation, i. Sign up to join this community. The best answers are voted up and rise to the top.
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Viewed k times. Mahmoud Ahmed Mahmoud Ahmed 2 2 gold badges 7 7 silver badges 8 8 bronze badges. I wonder. Maybe you have a point. Add a comment. Active Oldest Votes. Fly by Night Fly by Night We leave the logarithm undefined in that case, as you said in your original question: the logarithm is only defined for a positive base.
Show 2 more comments. Robin Robin 3 3 silver badges 3 3 bronze badges. I'm pretty sure it is not rigorous at all, but maybe it will be easier to remind? Thank you for your comments. BLAZE 8, 13 13 gold badges 39 39 silver badges 87 87 bronze badges.
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