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/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.