What is the answer for this? Write the expression in terms of $\log x$ and $\log y$ $$\log\left(\dfrac{x^3}{10y}\right)$$

This is what I got out of the equation so far. the alternate form assuming $x$ and $y$ are positive $$3\log(x)-\log(10y)$$ or maybe $$\log\left(\dfrac{x^3}{y}\right)-\log(5)=\log(2)$$?

I would appreciate a solution or an input thanks so much.


As you have your answer I will simply give some help for future.

There are 3 basic(1,2 and 3) formula regarding logarithm:

1.$\ log_am+\ log_an=\ log_a(mn)$

2.$\ log_am-\ log_an=\ log_a(\dfrac {m}{n})$

3.$\ log_am^n=\ n\times\ log_a(m)$

4.$\ log_aa=1$

5.$\ log_ab\times \ log_na=\log_nb$

6.$\dfrac {\ log_am}{\ log_an}=\ log_nm$

and the basic which useful for solving log equation

$\log_{a}{b}=n\Longleftrightarrow a^n=b$

These can solve many problems regarding logarithm.


I think you are close to the expected answer with your first answer. That is, $$\log\left(\frac{x^3}{10y} \right) = \log(x^3) - \log(10y) = 3 \log(x) - \log(10) - \log(y).$$


\begin{align*} \log (\frac{x^3}{10y}) & = \log (x^3) - \log (10y) \\ & = 3 \log x - (\log 10 +\log y) \\ & = 3 \log x - \log 10 - \log y \end{align*} using $$ \log(ab) = \log a + \log b ,$$ $$ \log(\frac{a}{b}) = \log a - \log b $$ and $$ \log(a^n) = n \log a $$


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.