Question

5^(x+2)=3^(x)

Answer 1

Okay, I'm not sure how you would do this without taking logs, so you're gunna have to do it even if you're not too comfortable with it.

Answer 2

So, (x+2) log(5) = x log(3)

Answer 3

It's going to be just an algebra problem from here.

Answer 4

(x+2)/x = log(3)/log(5)

Answer 5

Which becomes

1+(2/x) = .6826061945

Answer 6

Subtract the one and then multiply both sides by x

Answer 7

-3.173938x = 2

So x = 2/(-3.173938)

Answer 8

Or you could just leave the logs as is if you want an exact answer. Not sure how your teacher likes their answers.

Answer 9

You can double check your answer by just plugging your result back in to both sides of the equation.

Answer 10

And it looks like I did it right, but you can varify for your self.

Answer 11

2/-3.2 for the final answer? it seems to check out mathematically

Answer 12

Yeah. About that.

Answer 13

It does involve rounding, so you could have just left the logs in their original form for an exact answer.

Answer 14

wait

Answer 15

so log(2)/log(-3.2)?

Answer 16

No. you can't take the logarithm of a negative number (well, you might be able to and get some imaginary number, but I dunno)

Answer 17

1+ (2/x) = log(3)/log(5)

Answer 18

(2/x) = log(3)/log(5) -1

Answer 19

i plugged the 2/-3.2 in to the original problem and it wasn't even close. so i think the logs have to be in there somewhere, I'm just not sure where

Answer 20

2/-3.2 doesn't work?

Answer 21

no. i got .5 something. unless i entered it wrong, ill try again

Answer 22

Nah you're right

I'll check to see where I went wrong.

Answer 23

yeah i got the same answer. hmm lemme see

Answer 24

Oh wait it's 2/-.32

Answer 25

No 2/-3.2

Answer 26

My bad small typo.

Answer 27

x=−2ln(5)ln(5)−ln(3)
x≈−6.301320206174

Answer 28

?

Answer 29

Yeah, -6.301 is about equal to 2/-.32

Answer 30

gotcha. alright next problem. are you getting tired of this yet? lol

Answer 31

It's fine. I might have to leave soon though.

Answer 32

no problem buddy. just let me know, i really appreciate this

Answer 33

you any good at story problems?

Answer 34

Eh, they're annoying. Go ahead and post it and I'll see what I can do.

Answer 35

well i have others too, but ill throw one up