Use the properties of logarithms to simplify the expression by eliminating all exponents and radicals.
Assume that .

Ask by Reyes Phillips. in the United States

Mar 12,2025

Question

Use the properties of logarithms to simplify the expression by eliminating all exponents and radicals. Assume that $$ x, y>0 $$. $$ \log \left(x^{2} y^{3}\right)=\square $$

UpStudy AI · Accepted Answer

We start with the expression

$$
\log\left(x^2y^3\right)
$$

Using the logarithmic property that relates the logarithm of a product to the sum of logarithms,

$$
\log(ab) = \log a + \log b,
$$

we can write

$$
\log\left(x^2y^3\right)=\log\left(x^2\right)+\log\left(y^3\right).
$$

Next, we use the logarithmic power rule,

$$
\log(a^b)=b\log a,
$$

to handle the exponents:

$$
\log\left(x^2\right)=2\log x \quad \text{and} \quad \log\left(y^3\right)=3\log y.
$$

Thus, the expression simplifies to

$$
\log\left(x^2y^3\right)=2\log x + 3\log y.
$$
$$ \log\left(x^2y^3\right) = 2\log x + 3\log y $$

Use the properties of logarithms to simplify the expression by eliminating all exponents and radicals.
Assume that .

Upstudy AI Solution

Answer

Solution

Beyond the Answer

Related Questions

Latest Algebra Questions

Use the properties of logarithms to simplify the expression by eliminating all exponents and radicals. Assume that .