## anonymous one year ago Express the following in terms of log x. log x^3/2 + log cube root of x I don't know how to solve this, please help!

1. anonymous

$\log x ^{\frac{ 3 }{ 2 }} + \log \sqrt[3]{x}$

2. anonymous

another one i am stuck on: $3 \log x + \log x ^{3}$

3. Nnesha

familiar with the log rules ?

4. Nnesha

quotient rule$\large\rm log_b x - \log_b y = \log_b \frac{ x }{ y}$ to condense you can change subtraction to division product rule $\large\rm log_b x + \log_b y = \log_b( x \times y )$ addition ----> multiplication power rule $\large\rm log_b x^y = y \log_b x$

5. Nnesha

$$\color{blue}{\text{Originally Posted by}}$$ @Zas $\log x ^{\frac{ 3 }{ 2 }} + \log \sqrt[3]{x}$ $$\color{blue}{\text{End of Quote}}$$ there is plus sign so which rule would you apply ?

6. anonymous

So you would multiply them?

7. Jhannybean

use the multiplication rule: $$\sf \log(a) + \log(b) = \log(a\cdot b)$$ First start by changing $$\sf \log\sqrt[3]{x}$$ into a cubic power. : $$\sf \log(x)^{1/3}$$ Now apply multiplication property: $$\log(x)^{3/2} + \log(x)^{1/3} = \log(x^{3/2} \cdot x^{1/3}) =\log(x^{3/2 +1/3})$$

8. Jhannybean

What is $$\dfrac{3}{2} +\dfrac{1}{3}$$ ?

9. anonymous

11/6, thank you so much!