Axion's C2 questions

Hi guys,

got a c2 exam in less than 2 weeks, and really not understanding the methodology involved with doing well in some questions.
If its ok, i'll dedicate this thread to my queries rather than to clog up the board.

- The graph of y=a(b^x) passes through (1,6) and (2,3.6). Find the values of a and b

I logged both sides to get logy = log a + xlogb and then input the coordinates given to form two separate equations:

log6 = loga + logb
log3.6 = loga + 2logb

Where do I go from here?

Reply 1

sputum

9

logs aren't my strong point :frown:

but you can solve this one without them.

6 = a(b¹)
3.6 = ab²

I wouldn't take logs to start with, mash the algebra around a bit first and only introduce logs when you need to.

Reply 2

Axion

OP

15

HMm, its just as I said I dont quite get the emthodology but my first instinct was to log it and it must be possible my way.

Answers are a = 10 and b =0.6

But how do I get them?

Reply 3

raheem94

13

Original post by Axion

Hi guys,

got a c2 exam in less than 2 weeks, and really not understanding the methodology involved with doing well in some questions.
If its ok, i'll dedicate this thread to my queries rather than to clog up the board.

- The graph of y=a(b^x) passes through (1,6) and (2,3.6). Find the values of a and b

I logged both sides to get logy = log a + xlogb and then input the coordinates given to form two separate equations:

log6 = loga + logb
log3.6 = loga + 2logb

Where do I go from here?

You have got 2 equations.

log6 = loga + logb \longrightarrow (1) \\ log3.6=loga+logb^2 \longrightarrow (2)

Subtract both equations,

log6-log3.6 = loga + logb - loga-logb^2

Remember,

\displaystyle logc - logd = log\left(\frac{c}{d} \right)

Do you get it?

Reply 4

sputum

9

6 = ab
3.6 = ab²

a=b/6 (from 1)

3.6 = (b/6)(b²) (substituting for a in 2)
or you can divide equation (2) by (1)

if you must use logs, raheem's solution looks great

Reply 5

Notnek

21

Original post by Axion

HMm, its just as I said I dont quite get the emthodology but my first instinct was to log it and it must be possible my way.

Answers are a = 10 and b =0.6

But how do I get them?

Yes you can do it using logs as Raheem has showed you but you should understand that you can solve the equations quite easily without using logs.

Look at the equations given by Sputum. If you multiply the first one by b you get

\displaystyle 6b = ab^2

Now if you compare this with the second equation, it should be clear that

\displaystyle 6b=3.6

It's simple from here.

Reply 6

Extricated

17

You don't even need logs for this..

6 = ab ==> a = 6/b (*)
3.6 = ab^2 (2)

substituting (*) into (2)

3.6 = (6/b)(b^2)

so 3.6 = 6b^2/b then its easy to solve for b, then sub into (*) to get a.

edit : too slow