Question

Need help solving logarithm equation.!

Answer 1

\[2 ^{2x-5}=7^{3x-7}\]

Answer 2

So you want to evaluate for the powers, the first thing you want to do is take the log of both sides Do you know how to do this?

Answer 3

Not really! does that make the power go down so 2x-5log2 ?

Answer 4

You are correct :)

Answer 5

Now do the same thing o the other side~

Answer 6

2x-5log2 = 3x-7log7

Answer 7

Good job. Now you want to expand both sides of the equation by multiplying \(\log(2)\) and \(\log(7)\) into their respected functions :)

Answer 8

So \[\log(2)(2x-5) = \log(7)(3x-7)\] and expand these out :)

Answer 9

how do I expand?

Answer 10

Treat \(\log(2)\) and \(\log(7)\) like constants, so just distribute them :)

Answer 11

Let me know what you get! :D

Answer 12

2xlog2-5log2=3xlog7-7log7

??

Answer 13

Awesome! :D You're a really fast learner.

Answer 14

Yes you are right.

Answer 15

Now subtract \(\sf -3x\log(7)\) to both sides and add \(\sf +5\log(2)\) to both sides. What does your equation become?

Answer 16

2xlog2=-7log7

Answer 17

Not quite.

Answer 18

ok now im lost haha

Answer 19

2xlog2 - 5log2 = 3xlog7 - 7log7
+ 5log2 +5log2
_________________________________________

2xlog2 + 0 = 3xlog7 - 7log7 + 5log2
-3xlog7 -3xlog(7)
_________________________________________

2xlog(2) - 3xlog(7) = 0 -7log(7) + 5log(2)

Answer 20

ok but that just moves them to the opposite sides? what do i do after that?

Answer 21

Now that we've got all our log functions with x's on one side, and the constants on the other side, what would the equation look like if you factored out the x from the left side?

Answer 22

Oh I see! so then x(2log2)-(3log7)

Answer 23

and then I just plug it in the calculator and solve for x right?

Answer 24

yes :) x(2log(2) - 3log(7))

Answer 25

Next step is to divide both sides of the equation by `2log(2)-3log(7)`

Answer 26

What does your equation look like then

Answer 27

x=-7log(7)+5log(2)

Answer 28

Not quite! We have \[\sf 2x\log(2) - 3x\log(7) = 0 -7\log(7) + 5\log(2)\]We factored out an x\[x(2\log(2) -3\log(7)= -7\log(7)+5\log(2)\]Then we divde both sides ofthe equation by `2log(2)-3log(7)`\[\frac{x(2\log(2)-3\log(7))}{2\log(2)-3\log(7)}=\frac{-7\log(7)+5\log(2)}{2\log(2)-3\log(7)}\]We end up with \[x=~?\]

Answer 29

Do you understand what I did? @bgarcia907 ?

Answer 30

Yes I see. so then just evaluate the right side? so x=-8.2244

Answer 31

Im getting a positive answer.

Answer 32

Are you plugging in your parenthesis correctly?

`( -7 * log(7) + 5 * log(2) ) / (2 * log(2) - 3 * log(7) )`

Plug it in to your calculator that way ^

Answer 33

I did that and go 2.2814
is that what you got?

Answer 34

There you go :)

Answer 35

Good job working this out so quickly!

Answer 36

Thank you! You were of great help!

Answer 37

Thanks! :)