Question

easy little question ;)

What is the solution to the equation?

Answer 1

I start by taking the log of both sides
\[\log{\big({\frac{3}{2}x+\frac{7}{2}}\big)=x \log{2} }\]

Answer 2

add the fractions inside the log on the left side

Answer 3

o_O

Answer 4

can we go bit slower ;)

Answer 5

7/2 ?

Answer 6

noo, what about the x

Answer 7

i dunno

Answer 8

Or I guess we could multiply by two first:

\[{2*\big({\frac{3}{2}x+\frac{7}{2}}\big)=2*{2^x} }\]

Answer 9

wats the log, :O im slow at maths :(

Answer 10

i never seen this kind of question b4

Answer 11

6/4x + 14/2 ?

Answer 12

\[{\big({3x+7}\big)=2^{x+1} }\]
\[\log{\big({3x+7}\big)=\log{2^{(x+1) }} }\]

Answer 13

so 2 is the log ?

Answer 14

so 2 cznceleachother out?

Answer 15

6x + 14 = 2x ?

Answer 16

The log is a function which has some interesting exponential properties. If it is unfamiliar to you then perhaps guess and check makes more sense, actually. x is going to be an odd number if it has an integer solution.

Answer 17

ahh, wats the annswer?

Answer 18

Check the first few odd numbers and you will find it.

Answer 19

x = 3?

Answer 20

Yes. It has to be odd because 3x+7 must equal a product of 2, hence even.

Answer 21

And this problem is not easy if we change the fractions even a little bit because it escapes the integers.

Answer 22

But this is actually the foundation of some pretty cool math around encryption methods. (rational points on elliptic curves if you are interested)