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Chapter 13: Problem 19

Write as the sum or difference of logarithms and simplify, if possible. Assume all variables represent positive real numbers. $$\log _{3} \sqrt{7}$$

Short Answer

Expert verified
\(\frac{1}{2} \log _{3}(7)\)

Step by step solution

01

Identity: Logarithm of a root

To simplify this expression, we will first use the property \(\log_a \sqrt[n]{x} = \frac{1}{n}\log_a x\). In our case, we have the square root, so we will set n = 2: \(\log _{3} \sqrt{7} = \frac{1}{2} \log _{3}(7)\)
02

Answer

After applying the logarithm property, we see that our simplified expression is: \(\frac{1}{2} \log _{3}(7)\) This is the final answer as the sum or difference of logarithms.

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Most popular questions from this chapter

Find the inverse of each one-to-one function. $$h(x)=\sqrt[3]{x-7}$$

Find the inverse of each one-to-one function. $$g(x)=-4 x+8$$

Solve equation. \(\log _{2} r+\log _{2}(r+2)=3\)

Given that \(\log 5=0.6990\) and \(\log 9=0.9542,\) use the propertics of logarithms to approximate the following $$\log 25$$

Find the inverse of each one-to-one function. Then, graph the function and its inverse on the same axes. $$g(x)=\sqrt[3]{x}+4$$
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