# Thread: Rearranging log equation 2

1. ## Rearranging log equation 2

How do I rearrange this for y?

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

thx

2. ## 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

3. ## Re: Rearranging log equation 2

Sorry I didn't realise.
I did mean base 10 thx

4. ## Re: Rearranging log equation 2

log(y/x^3)=10^2

5. ## Re: Rearranging log equation 2

Recall that $y= 10^{log(y)}$. Does this give you any ideas how to simplify the LHS?

-Dan

6. ## Re: Rearranging log equation 2

Hello, JellyOnion!

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

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

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

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

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

Therefore:. . . $y \;=\;100x^3$

7. ## 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

8. ## Re: Rearranging log equation 2

Thank u everyone, much appreaciated