Use properties of logarithms to condense the logarithmic
expression. Write the expression as a single logarithm whose
coefficient is 1 Where possible, evaluate logarithmic
expressions.

(Use parentheses to clearly denote the argument of
each function.)

Ask by Elliott French. in the United States

Mar 23,2025

Question

Use properties of logarithms to condense the logarithmic
expression. Write the expression as a single logarithm whose
coefficient is 1 Where possible, evaluate logarithmic
expressions.

(Use parentheses to clearly denote the argument of
each function.)

Ask by Elliott French. in the United States

Mar 23,2025

UpStudy AI · Accepted Answer

We start with the expression:
$$
\frac{1}{2}\left(\log_{4} s + \log_{4} t\right)
$$

**Step 1.** Combine the logarithms inside the parentheses using the property:
$$
\log_b m + \log_b n = \log_b (mn)
$$
This gives:
$$
\log_{4} s + \log_{4} t = \log_{4} (st)
$$

**Step 2.** Now, multiply the logarithm by the coefficient $$\frac{1}{2}$$ using the property:
$$
a \cdot \log_b x = \log_b \left(x^a\right)
$$
Thus:
$$
\frac{1}{2}\log_{4} (st) = \log_{4} \left((st)^{\frac{1}{2}}\right)
$$

**Step 3.** Recognize that $$(st)^{\frac{1}{2}}$$ is the square root of $$st$$:
$$
(st)^{\frac{1}{2}} = \sqrt{st}
$$

So, the final condensed form is:
$$
\log_{4} \left(\sqrt{st}\right)
$$
$$ \log_{4} \left(\sqrt{st}\right) $$

Use properties of logarithms to condense the logarithmic
expression. Write the expression as a single logarithm whose
coefficient is 1 Where possible, evaluate logarithmic
expressions.

(Use parentheses to clearly denote the argument of
each function.)

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Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1 Where possible, evaluate logarithmic expressions. (Use parentheses to clearly denote the argument of each function.)

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Solución

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preguntas relacionadas

Latest Algebra Questions

Use properties of logarithms to condense the logarithmic
expression. Write the expression as a single logarithm whose
coefficient is 1 Where possible, evaluate logarithmic
expressions.

(Use parentheses to clearly denote the argument of
each function.)