Question

PLEASE HELP
1. 2 log x = 3 log 5

Answer 1

@SolomonZelman

Answer 2

i think the next step would be log x^2 = log 5^3

Answer 3

and then maybe next would be log x^2 = log 125 but i'm not sure about this step or what to do next...

Answer 4

log base 10?

Answer 5

Or natural log?

Answer 6

log base 10

Answer 7

i think...

Answer 8

@zepdrix

Answer 9

So 2logbase10 of x = 3logbase10 of 5

Answer 10

yes

Answer 11

Do you know about natural logs?

Answer 12

my teacher tried to teach me but honestly im confused

Answer 13

The latter half of the equation is saying 3 times 10 to what exponent equals 5

Answer 14

Oh sorry I ran off for a bit :D

So you need to apply your Log-Exponent Rule: \(\rm b\cdot\log(a)=\log(a^b)\)
\[\large\rm 2\log(x)=3\log(5)\]Applying this rule to the left side of the equation gives us,\[\large\rm \log(x^2)=3\log(5)\]Understand how you can apply it to the other side as well?
Try it! :)

Answer 15

3 times 10^x = 5 == 3logbase10 of 5

Answer 16

log 5^3 @zepdrix

Answer 17

So to solve for x divide by 3 than take the natural log of both sides.

Answer 18

\[\large\rm \log(x^2)=\log(5^3)\]Good good good.
Now notice that the logs are the same,
so the insides must equal as well,\[\large\rm x^2=5^3\]

Answer 19

so it has to be x^2 = 125

Answer 20

Yes, then solve for x.

Answer 21

or that a way

Answer 22

its a decimal. is that okay?

Answer 23

I dunno, you'll have to read your instructions for that,
exact form, or decimal approximation.

Answer 24

One thing to note:
Usually when you take a square root, you get a plus/minus for solutions.\[\large\rm x=\pm\sqrt{125}\]But notice that x=-sqrt(125) does NOT work for our original problem.
You can't take the log of a negative value.
So this solution is `extraneous`, just ignore it.
Only positive root works.

Answer 25

thanks for the help. mind helping with a few more?

Answer 26

Eh I'll be around :)
Open up a new thread, I'll stop by if I can find time.

You can @zepdrix and I'll try to find it.

Answer 27

thanks :)