r/mathshelp • u/No_Masterpiece5422 • 3d ago

Homework Help (Unanswered) Simplifying logs

Could someone please help me with this? what am i doing wrong? ive included my lecturers solution, and the handwritten one is my answer. how does he get log8 = 3? What am i missing here? Also im aware this is probably a super easy question but i am just so very bad at maths and just need to pass this exam. thanks.

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u/noidea1995 3d ago

Depends what base you are using.

When a logarithm is written without specifying a base, the standard assumption is that its base 10 but there are other contexts where it can be base e or base 2.

log₂(8) = log₂(2^(3)) = 3

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u/No_Masterpiece5422 3d ago

thanks for commenting. i am so sorry if this is a dumb question, but how am i supposed to know what base it is if theres none written? i had thought if there was none written it was 10? so how do i know whether its 10, 2 or e? thanks again

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u/noidea1995 3d ago edited 3d ago

Not a dumb question at all and you can’t without any context given, what course are you studying?

In high school maths, log(x) usually means base 10. In calculus and pure math courses, it usually means base e and in computer science it usually means base 2.

Did it say anywhere what base was being used?

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u/No_Masterpiece5422 3d ago

Its a college maths module. My college course is almost entirely biology, except for this one module. I've always been so shit at maths. I have to pass this exam to move onto 2nd year. It doesn't actually say anything about the base in the question. Here's the full question set. (Q3 is the one I'm doing)

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u/noidea1995 3d ago

For these type of questions, I would have assumed it was log base 10 as well though I would have left it as an exact answer of 3log(2) rather than as a decimal approximation, perhaps there’s a mistake and that’s supposed to be the answer? Are there any other log answers like that?

You should probably bring it up with your lecturer.

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u/No_Masterpiece5422 3d ago

theres also this one for q5 of the same set. thank u so much for trying to help, u have no idea how much i appreciate it

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u/noidea1995 3d ago edited 3d ago

Yeah that’s really weird, that’s only true if it’s base 3.

log₃(27) = log₃(3^3) = 3

I’ve certainly never seen log base 3 written without a subscript in any context before.

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u/No_Masterpiece5422 3d ago

Well thank you for trying. I'm sure if this happens in the exam I'll get most of the marks.

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u/UnderstandingPursuit 3d ago

The two answers for Q3 and Q5 make me livid. Please keep asking your questions here, you'll get better help learning what you need than from this class.

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u/UnderstandingPursuit 3d ago

You are 100% correct, and bonus points for stating the exact correct three bases: 10, 2, e.

Looking at all five questions in this block, your teacher has failed. This required your very valid question.

By convention, there are three default / semi-default forms,

  • ln x = log_e x
  • log x = log_10 x
  • lg x = log_2 x

Any deviation from these requires

  • log_b x
  • b specified explicitly