Question

Condensing Logarithmic Expression In Exercise,use the properties of logarithms to rewrite the expression as the logarithm of a single quantity.See example 4.
3/2[In x(x^2 + 1) - In(x + 1)]

Answer 1

Answer:

$[ln \frac{x(x^2 + 1)}{(x + 1)}]^\frac{3}{2}$

Step-by-step explanation:

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

ln(m/n)= lnm - ln(n)

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

$\frac{3}{2}[ln \frac{x(x^2 + 1)}{(x + 1)}]$

3/2 is before ln. so we move the fraction 3/2 to the exponent

as per log property we move the fraction to the exponent

$[ln \frac{x(x^2 + 1)}{(x + 1)}]^\frac{3}{2}$