Masha Hamid Has a Question on Logarithm

Mashal Hamid <mashalhamid.xx@gmail.com>	8:08 PM (3 hours ago)
to me

Hello Mr.Tan 

I was wandering if you could give me the solution to this question 16 from past year paper on logarithmic functions and indices, that i found on your blog, as I am having troubles with part (c) .

I would really appreciate it. 

Thanks. 

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Hello Mashal,

My proposed solution to part (c) is as follows:

Use the given f(x) = 2xlog_x3 – 5log_x9 – x + 5 to factorise into:

                     f(x) = (x – 5)(alog_x3 – b),

then the values of a and of b should be obvious as follows:

f(x) = 2xlog_x3 – 5log_x9 – x + 5

       = 2xlog_x3 – 5log_x3² – x + 5

       = 2xlog_x3 – 10log_x3 – x + 5

       = (2xlog_x3 – x) – (10log_x3 + 5)        ~ rearrange to factorise

       = x(2log_x3 – 1) – 5(2log_x3 - 1)

       = (x – 5)(2log_x3 – 1)

      [≡(x – 5)(alog_x3 – b)]

Hence, a = 2 and b = 1.

Hope the above helps. Have a good day!

J

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Mashal Hamid	Sep 19 (2 days ago)
to me

Yes, thank you so much, sir.