# Thread: Question on Logs

1. ## Question on Logs

When I try and solve the following I get the answer as log (x^-7/12)

1/3log(x^2) + log x - 3/4 log (x^3)

In the book it says log (x^1/12)

2. Originally Posted by davyboy123
When I try and solve the following I get the answer as log (x^-7/12)

1/3log(x^2) + log x - 3/4 log (x^3)

In the book it says log (x^1/12)
Note that, by the property $\displaystyle n \log X = \log X^n$, you have $\displaystyle \log x^{2/3} + \log x + \log x^{-9/4}$. Now use the property $\displaystyle \log X + \log Y = \log XY$

3. Originally Posted by davyboy123
When I try and solve the following I get the answer as log (x^-7/12)

1/3log(x^2) + log x - 3/4 log (x^3)

In the book it says log (x^1/12)
I agree with you ...

$\displaystyle \frac{1}{3}\log(x^2) + \log{x} - \frac{3}{4}\log(x^3)$

$\displaystyle \log(x^{\frac{2}{3}}) + \log{x} - \log(x^{\frac{9}{4}})$

$\displaystyle \log\left(\frac{x^{\frac{2}{3}} \cdot x}{x^{\frac{9}{4}}}\right)$

$\displaystyle \log\left(\frac{x^{\frac{5}{3}}}{x^{\frac{9}{4}}}\ right)$

$\displaystyle \log\left(\frac{x^{\frac{20}{12}}}{x^{\frac{27}{12 }}}\right)$

$\displaystyle \log\left(x^{-\frac{7}{12}}\right)$

... books have been wrong before.

4. Originally Posted by davyboy123
When I try and solve the following I get the answer as log (x^-7/12)
Originally Posted by davyboy123
1/3log(x^2) + log x - 3/4 log (x^3)
In the book it says log (x^1/12)

Hi all
another methode