Maths question?

Question

how to i answer this sort of question? :
Investigate the relationship between a and be if:
(3a)b = 2a + b
I don't understand how to answer this question.
P.S the a and the b are supposed represent indices but i couldnt get a symbol similar so i just put a and b.
Please help!

but i don't no what a and be equal! it doesnt say!

I am only in year nine and im pretty sure they don't expect us to do what you trying to say, it says explain the relationship it means like what does a have in common with b?

Answer 1

(3a)b = 2a + b
3ab - 2a = b
a(3b - 2) = b
a = b / (3b - 2)
<<< The equation above expresses the relationship between and b.

a = 0, b = 0
a = 1, b = 1
a = 0.5, b = 2
a = 3/7, b = 3 .... and so on

Answer 2

A lot of people use the ^ character for indices. You say that a and b are indices. Is your expression:

(3^a)^b = 2^(a+b)
or
(3^a)^b = 2a + b

or something else? If its one of the above it looks as though you may need to use logs. Have you studied this yet?

Answer 3

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Answer 4

if you have to find a in terms of b...
then take the terms containing a on one side of the equation..
after that take a common..
then take the terms containing b again on one of the sides..
and you will get a in terms of b

for eg.-in this case
(3a)b = 2a + b
(3a)b - 2a = b
a(3b - 2) = b
a = b/(3b -2)...which is the required answer

you can follow the same procedure to find b in terms of a..
the answer you wil get in this case is..
b = a/(3a-1)

have a nice day ツ

Answer 5

Looking at good stuff from aj and wordsmit... I notice that if a=I/3 then the term on the right has a zero denominator, so that b(on the left) tends to infinity as a approaches 1/3.
Just thought I'd say........

Answer 6

Remove brackets:
3b*ab = 2a + b,
3*a*b*b= a*a + b,
divide both sides by a,
3*b*b = a + b,
subtract b from b. s.
a =(3b^2) -b
a is greater than b.

Answer 7

You can plot them on a graph for various values of a, eg

if a=1 , then (3x1)xb=(2x1)+b => 3b=2+b => 2b=2 => b=1

if a=2, then (3x2)xb=(2x2)+b => 6b=4+b => 5b=4 => b=0.8

if a=3, then (3x3)xb=(3x2)+b => 9b=6+b => 8b=6 => b=0.666

if a=4, then (3x4)xb=(4x2)+b => 12b=8+b => 11b=8 => b=0.7272

It looks as though as a tends to infinity b tends to zero.

You'll need to check my arithmetic I did it quickly.

Answer 8

find what a equals then find what b equals then just explain the relationship between them :D