# Solve this NECO past questions 2016/2017

**Geaty**Member- Posts : 36

Q7a) Find d value of n if

3

7b) Solve d eqn:

log(x

Q9a) A two-digit number is such that its tens digit is greater than its unit digit by 5. If d number is 14 less than 3 times d product of its digits, find d numbers

3

^{2n+1}- 4(3^{n+1}) + 9 = 07b) Solve d eqn:

log(x

^{2}+4) = 2 + logx - log20Q9a) A two-digit number is such that its tens digit is greater than its unit digit by 5. If d number is 14 less than 3 times d product of its digits, find d numbers

**Admin**Administrator- Posts : 180

Log(x

log(x

log(x

20

Now, you cross multiply

given you 20(x

20x

now divid by 20

~~20~~ ~~20~~ ~~20~~

x

x

(x

x(x - 4) -1(x - 4)

(x - 1)(x - 4)

x = 1 or 4

^{2}+ 4) = 2 + log^{x}- log^{20}log(x

^{2}+ 4) = log^{100}+ log^{x}- log^{20}log(x

^{2}+ 4) = log (__100 X__)*x*20

Now, you cross multiply

given you 20(x

^{2}+ 4) = 100 X*x*20x

^{2}+ 80 = 100xnow divid by 20

__/ -__~~20x~~^{2}

__+__~~100x~~__= 0__~~80~~x

^{2}- 5x + 4 = 0x

^{2}- 4x - x + 4 = 0(x

^{2}- 4x)(x + 4)x(x - 4) -1(x - 4)

(x - 1)(x - 4)

x = 1 or 4

Last edited by Paradise on 29th June 2016, 9:22 am; edited 1 time in total

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**Geaty**Member- Posts : 36

3

Note that

3

while

4(3

Now

3(3

3(3

Let us call 3

therefore 3y

Divide by 3

~~3 ~~ ~~3~~ ~~3~~

we will have

y

y

(y

y(y - 3) - 1(y - 3)

(y - 1)(y - 3)

y=1 or 3

therefore when y=1

3

n = 0

when y = 3

3

n = 1

^{2n+1}- 4(3^{n+1}) + 9 = 0Note that

3

^{2n+1}= 3^{1}.3^{2n}= 3^{1}.(3^{n})^{2}while

4(3

^{n+1}) = 4(3^{1}.3^{n})Now

3(3

^{n})^{2}- 4 x 3(3^{n}) + 9 = 03(3

^{n})^{2}- 12(3^{n}) + 9 = 0Let us call 3

^{n}= ytherefore 3y

^{2}- 12y + 9 = 0Divide by 3

__-__~~3y~~^{n}

__+__~~12y~~__= 0__~~9 ~~we will have

y

^{2}- 4y + 3 = 0y

^{2}- 3y - y + 3 = 0(y

^{2}- 3y)(-y +3)y(y - 3) - 1(y - 3)

(y - 1)(y - 3)

y=1 or 3

therefore when y=1

3

^{n}= yn = 0

when y = 3

3

^{n}= yn = 1

__n= 0 or 1 Answer__**Wimpy**Member- Posts : 27

Very cool

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