Question

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!

Answer 1

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

Answer 2

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

Answer 3

familiar with the log rules ?

Answer 4

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 \[\large\rm log_b x^y = y \log_b x\]

Answer 5

\(\color{blue}{\text{Originally Posted by}}\) @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 ?

Answer 6

So you would multiply them?

Answer 7

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:

\(\log(x)^{3/2} + \log(x)^{1/3} = \log(x^{3/2} \cdot x^{1/3}) =\log(x^{3/2 +1/3})\)

Answer 8

What is \(\dfrac{3}{2} +\dfrac{1}{3}\) ?

Answer 9

11/6, thank you so much!