Expand the Logarithmic Expression log of 5(x^3)/2xy^3

$\log (5) \frac{x^{3}}{2} x y^{3}$

Step 1

Combine $\log (5)$ and $\frac{x^{3}}{2}$ .

$\frac{\log (5) x^{3}}{2} x y^{3}$

Step 2

Multiply $\frac{\log (5) x^{3}}{2} x$ .

Combine $\frac{\log (5) x^{3}}{2}$ and $x$ .

$\frac{\log (5) x^{3} x}{2} y^{3}$

Raise $x$ to the power of $1$ .

$\frac{\log (5) (x^{1} x^{3})}{2} y^{3}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{\log (5) x^{1 + 3}}{2} y^{3}$

Add $1$ and $3$ .

$\frac{\log (5) x^{4}}{2} y^{3}$

Step 3

Combine $\frac{\log (5) x^{4}}{2}$ and $y^{3}$ .

$\frac{\log (5) x^{4} y^{3}}{2}$

Step 4

Reorder factors in $\frac{\log (5) x^{4} y^{3}}{2}$ .

$\frac{x^{4} y^{3} \log (5)}{2}$