Question

Solve equation: log18(4v+9)=log15(5v-10).
how would u solve this. please help

Answer 1

are 18 and 15 the base or is it just the natural log?

Answer 2

\[\log_{18}(4v+9) = \log_{15}(5v-10)\]Correct?

Answer 3

yes whpalmer4

Answer 4

and dreamer02

Answer 5

Well, I've done it graphically, but haven't figured out how to get an exact solution (or if it can be done)...

Answer 6

okay

Answer 7

I wonder if perhaps noting that 18 and 15 have a GCF of 3 and using the change of base formula might get you anywhere...

Answer 8

i wondering the same thing but im not sure

Answer 9

Nah, it doesn't seem to do the job...and even Mathematica doesn't seem to be able to find an exact solution. I guess you have to do it numerically or graphically

Answer 10

i would go with numerically

Answer 11

because it want's it to be solved not graphed

Answer 12

Then I guess you're trying to find the value of \(v\) such that \[\frac{\ln (9+4v)}{\ln 18} - \frac{\ln(5v-10)}{\ln 15} = 0\]

Answer 13

Look in the vicinity of \(v = 9\):

Answer 14

oh okay

Answer 15

Look here http://www.wolframalpha.com/input/?i=%28log_%2818%29+%284v%2B9%29%29%3D%28log_%2815%29+%285v-10%29%29

I don't think there is an analytic way of solving it sorry...

Answer 16

wait, i got it.

Answer 17

okay i kinda get it

Answer 18

what

Answer 19

so, to solve the problem, multiply @whpalmer4 's equation by log(18)*log(15)

Answer 20

the top part or everything

Answer 21

no, even that way won't work...

Answer 22

Not really necessary to do so, those are just constants, and they aren't going to bother your root finder...

Answer 23

i was thinking about using ln(a)-ln(b)=ln(a/b)=0 and from there a/b=1, but you still have the constants...

Answer 24

which then become powers... there just isn't a way of solving this analytically.

Answer 25

yea it looks like there is no way hah