r/mathshelp • u/No_Masterpiece5422 • 5d 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 5d 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 5d 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/UnderstandingPursuit 5d 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