Question

Condensing Logarithmic Expressions In Exercise, use the properties of logarithms to rewrite the expression as the logarithm of a single quantity.
4[In(x3 - 1) + 2 In x - In(x - 5)]

Answer 1

Answer:

$4ln [\frac{x^2 (x^3-1)}{x-5}]$

Step-by-step explanation:

For this case we have the following expression:

$4[ln(x^3-1) +2ln(x) -ln(x-5)]$

For this case we can apply the following property:

$a log_c (b) = log_c (b^a)$

And we can rewrite the following expression like this:

$2 ln(x) = ln(x^2)$

And we can rewrite like this our expression:

$4[ln(x^3-1) +ln(x^2) -ln(x-5)]$

Now we can use the following property:

$log_c (a) +log_c (b) = log_c (ab)$

And we got this:

$4[ln(x^3-1)(x^2) -ln(x-5)]$

And now we can apply the following property:

$log_c (a) -log_c (b) = log_c (\frac{a}{b})$

And we got this:

$4ln [\frac{x^2 (x^3-1)}{x-5}]$

And that would be our final answer on this case.