Question

@Satellite73

Could you help me with this one as well?

5^(2x+1)=9^(x+1)

Answer 1

start out the same way
what do you get?

Answer 2

(2x+1)ln5=(x+1)ln9

Answer 3

multiply out, this time on both sides

Answer 4

let me know what you get

Answer 5

and don't be confuse by the \(\ln(5)\) and \(\ln(9)\) treat them like \(a\) and \(b\)

Answer 6

ln10x+ln5=ln9x+ln9

Answer 7

oops \(\ln(5)\times 2x=2\ln(5)x\) not \(\ln(10)x\)

Answer 8

should be
\[2\ln(5)x+\ln(5)=\ln(9)x+\ln(9)\] now put each term with an \(x\) in it on one side of the equal side, the ones without an \(x\) on the other
it is your choice as to which one to use

Answer 9

let me know what you get
you are two steps away after that one

Answer 10

2ln5x-ln9x=ln9-ln5

Answer 11

ok two more steps
factor out the \(x\) on the left hand side

Answer 12

Then factor out an x?

Answer 13

yes!

Answer 14

then divide as the last step

Answer 15

So x =(ln9-ln5)/(2ln5-ln9)

Answer 16

yes that should do it.
not that hard when you know what to do right?

Answer 17

I don't completely understand why



oops ln(5)×2x=2ln(5)x not ln(10)x

Answer 18

log is a function, which is why when i write it i always wrote \(\ln(5)\) or \(\ln(x)\) rather than ln5 or lnx

Answer 19

in other words it is like \(f(x)\)
now you would not expect \(f(x)\times 2\) so be equal to \(f(2x)\)

Answer 20

and it is not true that \(\ln(5)\times 2=\ln(5\times 2)\) then are just different numbers for sure

Answer 21

you should get in the habit of writing \(\ln(x)\) and when you start trig write \(\sin(x)\) as well
if you teacher doesn't do it, it is out of laziness and then is very apt to confuse
we even say "log of 5" rather than "log 5"

Answer 22

That does help me with the confusion. I have been confused since we started this. I really appreciate your help and I WILL start writing it ln(x)

Answer 23

good, and good luck. once you get the hang of it, it is not that hard
also notice that after step 1, which you did on your own, it was algebra from there on in and had nothing really to do with logs