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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: TyranT on July 23, 2019, 05:59:16 am

Title: Few questions need help with
Post by: TyranT on July 23, 2019, 05:59:16 am: I have 3 questions i have attached. If anyone could help me with them, it would be much appreciated.

Thanks.
Title: Re: Few questions need help with
Post by: caffinatedloz on July 23, 2019, 06:59:47 am: Only in Year 10, so could not figure out 11, but question 10 just relies on using the log laws.

(https://i.imgur.com/xfhP1z3.jpg)
Title: Re: Few questions need help with
Post by: TyranT on July 23, 2019, 04:47:40 pm: Thanks alot!
Title: Re: Few questions need help with
Post by: fun_jirachi on July 23, 2019, 05:27:37 pm: Just to tack on to laura_'s answer, Q11 requires a little more manipulation.

Note that for any real positive numbers a, x and y, that if:
$y=a^x, \ \text{then} \ x=\log _a y$
Hence, 2=log₂4, since 2²=4. The key here is working towards using the same log law demonstrated in Q10 ie. ln(a)+ln(b)=ln(ab) by utilising the same log base for both expressions.

Your expression then becomes log₂y=log₂(x-1)+log₂4.

Try going from here :)
Title: Re: Few questions need help with
Post by: SmellsLikeTeenSpirit on July 30, 2019, 03:04:04 pm: Hi Tyrant,
Sorry for the delay. The step-by-step solutions are attached. Hope this may help.
Cheers