**如有雷同纯属巧合**

“*Miss Loi, I can’t come for tuition today! Coz … I … I … got a date 😛*”

“*Miss Loi, for the sake of my future PLEEEEEEZE excuse me from tuition today! I don’t wanna be a monk!*”

“*Miss Loi, today cannot come. Got char bor tonight.*” *hangs up abruptly* 😕

And so, armed with a sudden abundance of time after being predictably spurned by many of her students, Miss Loi decided to pack up early and drove leisurely to a “leisure & lifestyle destination” in a remote part of Singapore to relax and spend some time by herself.

Seated by a table at the local McDonald’s, she was soon starkly reminded of the significance of the day amid scenes of lovey-dovey couples around her in various stages of companionship.

Her state of loneliness was emphasized 1 × 10^{6} times as she watched, with a tinge of envy ~~and nostalgia~~, a couple shoving spoonfuls of McFlurry ice cream ‘romantically’ into each other’s mouths; a girl (pretending to be) pleasantly surprised by a bouquet of roses whipped out by her boyfriend … and a bunch of youths staring at her from two tables away.

After a thorough self-inspection of her face/eyes/hair/makeup/dress/shoes which failed to find any sort of stain that might have triggered their attention, she stared back at them in bewilderment.

But they simply continued to stare at her.

Feeling a bit annoyed by this, she stared back at them with greater ferocity ~~and laser beams shooting out from her eyes~~.

Suddenly one of the youths stood up, walked towards her, and asked her in Hokkien,

Miss, why you stare at us huh? What’s your number?

Miss Loi blushed a little before replying shyly,

Ooh you’re rather direct aren’t you? Don’t you think you’re a little too young for me?

His voice took on a rather unfriendly tone.

We are from the 4455 Society! Which society are you from?

Huh? Umm … errr … I’m from the Joss Sticks Society. Please like my Facebook page when you visit 😉

He looked a bit confused at first, but raised his voice nonetheless.

I’ve never heard of your stupid-sounding society, but this table belongs to our gang and society! Get lost now!

Boy was Miss Loi hopping mad now …

DO YOU HAVE TO BE SO RUDE?! I didn’t know McDonald’s sold their tables to SILLY groups like yours with a SILLY boy band-sounding name!

At that precise moment, the entire tattoo-laden detachment from the 4455 ~~boy band~~ Society rose up from their table, brandishing their steely choppers.

Miss, you dare to insult our Society’s name! We will take you to our Big Boss and let him deal with you!

Sensing that something was obviously very wrong, Miss Loi slowly inched her way away from the table. Her tentative steps turned into a trot, and before long her Charles & Keith shoes were off as she broke her own speed record multiple times running at full throttle past terrified onlookers to escape the chasing pack of youths.

Thanks to her infamous sense of direction, however, her escape was brought to a screeching halt when she ran into a dead end – where she ended up with her back pressed to the wall, eyes shut and head tilted to one side as she awaited her impending fate at the hands of the slowly-approaching mob.

STOP!!! This girl is mine!

A familiar face suddenly burst into the scene, surprising the mob.

I am a member of 4455. She is my girl. I will bring her to Big Boss myself!

Who are you? I’ve never seen you before. If you are really part of us then you should know our password.

…

Maybe you are still new. It’s OK, the password is the solution to this

challengingindices question – which all 4455 members should know how to solve since ours is an elite society! 4455! 4455!

^{x}= 32 and 43

^{y}= 32, find the value of .

When Miss Loi tried to answer, she was firmly put in her place.

Shut up Miss! Only he can answer this! Don’t think you can even solve it in your lifetime looking at your bimbo Ah Lian face!

And so, can you help Smiling 哥 finally, finally attain his wish of becoming his 梦中情人 Miss Loi’s hero on Valentine’s Day?

4455! 4455!

P.S. Please note that Miss Loi & the Joss Sticks Society does NOT advocate nor condone any form of secret society activities in Singapore.

## 13 Comments

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the answer is 0.8?

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@Sushila: One of the youths shouted

"WHERE'S YOUR WORKINGS??!!!"

😛

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@Miss Loi: Aiyoh....... *feeling my ears hurting* Anyway my working is same as mathslover's. That's how I arrived at this answer.

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x lg 688 = lg 32

x = lg 32 / lg 688

1/x = lg 688 / lg 32

y lg 43 = lg 32

y = lg 32 / lg 43

1/y = lg 43 / lg 32

1/x - 1/y = lg 688 / lg 32 - lg 43 / lg 32 = (lg 688 - lg 43)/lg 32 = 0.8

"It is 0.8! Now leave this lady alone!" Smiling 哥 jumped up and down infront of all the wide-mouthed 4455 people.

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@mathslover: Using log is one good way to get the answer. How about using purely indices to get 0.8?

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@Alex: Actually that was Miss Loi's original intention when she posted this indices question with an indices tag.

Oh should have added something like

"Smiling 哥 did not have a scientific calculator with him! ... and Miss Loi was not allowed to lend him hers ... and the gang did not allow him to use calculator anyway" 😛

P.S. If you solve via indices, chance are your final password should be rather more '4455-friendly' 😉

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@Miss Loi: Without using calculator, his way of solving log question will still be ok. But I really like the indices approach. It is challenging and stimulating. Where did you see this question from?

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@Alex: Ooooh wait wait wait wait wait ... missed the fact that 688 is divisible by 43 *

FACEPALM* so using the Laws of Logarithm:=

=

=

=

=

So it's ! No calculators! And it sounds like 4455!

But the youths didn't take AMaths (and this question is categorized under EMaths anyway) so they couldn't understand the logarithmic approach!😛And now they are sharpening their knives and demanding to see the 'stimulating' but still elusive Indices approach ...

P. S. This question was presented to Miss Loi in class by a decent-looking Sec Three youth (with no affiliation to the 4455 gang :P)

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@Miss Loi: miss loi has the solution right? basically, for e maths method, just make 43 the subject of the 2 equations and you can get the answer. It is really a brilliant and nice question. 🙂

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(43 × 16)

^{x}= 3243

^{x}= = 2^{5−4x}43

^{y}= 2^{5}-------------------

This is NOT part of the submitted working... 😛

xlg 43 = (5−4x) lg 2 --- (1)ylg 43 = 5 lg 2 --- (2)(1) div (2),

Ok to be honest I can't see how to get through here using laws of indices alone.

----------------------

5

x= 5y− 4xy曜

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@mathslover: well, most people will be stuck at the part of 43

^{x}= 2^{5−4x}. What you can do is make 43 the subject of the formula, which is. Then for the other equation 43

^{y}= 2^{5}. We can also make 43 the subject, which is . Since both equations are the same, . I believe that from here, you can get the answer right?曜

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@Alex: Urgh Alex why don't you just write your answer down and save Miss Loi the trouble of waiting for an elusive indices answer that refuses to appear? 🙂

What you had is (5-4x)/x = 5/y which, when cross multiplied, will give 5x = 5y-4xy, which is what I already have in post #3.

So, refer to that post for subsequent workings. Heehee...

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@mathslover: but i have already given the main part of the workings. After that, what we need to do is compare the powers since the base is the same. (5 - 4x)/x = 5/y.

5/x - 4 = 5/y

5/x - 5/y = 4

5(1/x - 1/y) = 4

1/x - 1/y = 4/5