Eric Nicholas K's answer to LockB's Secondary 3 A Maths Singapore question.
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Q12c
Date Posted:
3 years ago
i dont really understand what is going on here
btw we are allowed to add and subtract logarithmic forms?
btw we are allowed to add and subtract logarithmic forms?
why isnt 1 changed to log16 16 tho
Basically the first step which I did here is to convert all the bases into base 2 for such equation solving. Bases 10 and e are more of solving exponential equations.
Logarithms can be added and subtracted. In fact, the laws of logarithms contain such additions and subtractions.
For example,
log2 5 + log2 8 = log2 40.
Even things like log2 x + log2 x = 2 log2 x make sense, because this is just like k + k = 2k.
You can actually change the “1” to log16 16, but I decided to keep the 1 at the end so that I can convert the logarithmic form to exponential form. I always leave a number on one side (in this case, the number 1) for the calculation.
5/12 log2 x = 1
From here, by leaving the 1 on the RHS, we are almost ready to solve such equations by converting the form.
For example,
log2 5 + log2 8 = log2 40.
Even things like log2 x + log2 x = 2 log2 x make sense, because this is just like k + k = 2k.
You can actually change the “1” to log16 16, but I decided to keep the 1 at the end so that I can convert the logarithmic form to exponential form. I always leave a number on one side (in this case, the number 1) for the calculation.
5/12 log2 x = 1
From here, by leaving the 1 on the RHS, we are almost ready to solve such equations by converting the form.
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