Why does the base and number have to be positive for logs? (1 Viewer)

[anonymoushehe]

we started doing basics of logs at school, and was confused why the number and the base have to be greater than 0. Like for example if we have the number -8 and the base -2, wouldn’t the log be 3??

sorry if this sounds dumb

 

[synthesisFR]

we started doing basics of logs at school, and was confused why the number and the base have to be greater than 0. Like for example if we have the number -8 and the base -2, wouldn’t the log be 3??

sorry if this sounds dumb

try converting it to expnential

 

[howcanibesmarter]

we started doing basics of logs at school, and was confused why the number and the base have to be greater than 0. Like for example if we have the number -8 and the base -2, wouldn’t the log be 3??

sorry if this sounds dumb

becase ln 0 is undefined. try graphing lnx, where is its domain? Its (0 , infinity), so any number outside that domain i.e. -2,-8 remains undefined.

By change of base,
log(base-2) (-8) = ln(-8)/ln(-2), which is undefined by reasons above hope that makes sense.

 

[Eagle Mum]

log-2 (-8) isn’t defined in the real plane of numbers, but it is with complex (real + imaginary) numbers which is explored in Yr 12 extension 2 maths.

I highly recommend this YouTube video (www.youtube.com/watch?v=9D62oOf7k2A) for those who have already covered complex numbers, but this might be too early for you OP if you are doing stage 5 maths.

 

[howcanibesmarter]

log-2 (-8) isn’t defined in the real plane of numbers, but it is with complex (real + imaginary) numbers which is explored in Yr 12 extension 2 maths.

I highly recommend this YouTube video (www.youtube.com/watch?v=9D62oOf7k2A) for those who have already covered complex numbers, but this might be too early for you OP if you are doing stage 5 maths.

bruv is in yr10 and ur giving him complex thats diabolical

 

[Eagle Mum]

bruv is in yr10 and ur giving him complex thats diabolical

I did include ‘but this might be too early for you OP if you are doing stage 5 maths.’ It actually sounded like OP might be doing Yr 11 maths even though they are in Yr 10.

Generally, I think it’s a better approach to teaching to say ‘yes, you’re right, but that’s something you’ll learn about later’, than to say
‘no, because this is the rule (within the limited set of constructs to which they’ve been introduced)’ and then later introduce them to different sets of constructs. People who learn (or are taught) maths this way may do well at topic tests but may never appreciate that maths is universal.

 

[anonymoushehe]

I did include ‘but this might be too early for you OP if you are doing stage 5 maths.’ It actually sounded like OP might be doing Yr 11 maths even though they are in Yr 10.

Generally, I think it’s a better approach to teaching to say ‘yes, you’re right, but that’s something you’ll learn about later’, than to say
‘no, because this is the rule (within the limited set of constructs to which they’ve been introduced)’ and then later introduce them to different sets of constructs. People who learn (or are taught) maths this way may do well at topic tests but may never appreciate that maths is universal.

omg thats kinda like a compliment but im doing year 10 ty though omg