Expanding Logarithmic Expressions In Exercise, use the properties of logarithms to rewrite the expression as a sum, difference,

Question

3 years ago

8

or multiple of logarithms.
In (x^2(x - 1))1/2

1 answer:

aev [14] · Answer 1 · 2022-04-05T04:34:02+03:00

aev [14]3 years ago

6 0

Answer:

The simplified expression is:

$\ln{x} + \frac{\ln{(x-1)}}{2}$

Step-by-step explanation:

We have those following logarithmic properties:

$\ln{\frac{a}{b}} = \ln{a} - \ln{b}$

$\ln{a*b} = \ln{a} + \ln{b}$

$\ln{a^{n}} = n\ln{a}$

In this problem, we have that:

$\ln{x^{2}(x-1)}^{1/2}$

Applying these properties

$\frac{1}{2}*(\ln{x^{2} + \ln{(x-1)})$

$\ln{x} + \frac{\ln{(x-1)}}{2}$