# Rearranging log equation 2

• Jul 11th 2013, 07:23 PM
JellyOnion
Rearranging log equation 2
How do I rearrange this for y?

log(10)y=3log(10)x+2

thx
• Jul 11th 2013, 08:02 PM
ibdutt
Re: Rearranging log equation 2
In fact what you want is not clear
It may be written as
log 10y - 3 lof 10x = 2
log (10y)/( 1000 x ^3) = 2
If the log is to the base 10 then we have
(10y)/( 1000 x ^3) = 10 ^ 2 etc please be specific with your question so as to enable us to help and avoid guess work
• Jul 11th 2013, 11:27 PM
JellyOnion
Re: Rearranging log equation 2
Sorry I didn't realise.
I did mean base 10 thx
• Jul 12th 2013, 07:18 AM
ithanareshbabu
Re: Rearranging log equation 2
log(y/x^3)=10^2
• Jul 12th 2013, 07:38 AM
topsquark
Re: Rearranging log equation 2
Recall that $\displaystyle y= 10^{log(y)}$. Does this give you any ideas how to simplify the LHS?

-Dan
• Jul 12th 2013, 09:10 AM
Soroban
Re: Rearranging log equation 2
Hello, JellyOnion!

Since the base is 10 (ten), we can drop the subscript.

Quote:

$\displaystyle \text{Solve for }y\!:\;\log y \:=\:3\log x+2$

We have: .$\displaystyle \log y \;=\; 3\log x + 2\cdot 1 \;=\;3\log x + 2\log(10)$

. . . . . . . . $\displaystyle \log y \;=\;\log(x^3) + \log(10^2) \;=\;\log(x^3) + \log(100)$

. . . . . . . . $\displaystyle \log y \;=\;\log(100x^3)$

Therefore:. . .$\displaystyle y \;=\;100x^3$
• Jul 12th 2013, 09:34 AM
HallsofIvy
Re: Rearranging log equation 2
Or log(y)= 3log(x)+ 2 so log(y)- 3 log(x)= log(y/x^3)= 2
y/x^3= 100, y= 100x^3
• Jul 13th 2013, 06:07 PM
JellyOnion
Re: Rearranging log equation 2
Thank u everyone, much appreaciated