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Chapter 13: Problem 17

Write as the sum or difference of logarithms and simplify, if possible. Assume all variables represent positive real numbers. $$\log p^{8}$$

Short Answer

Expert verified
\(\log p^8 = 8 \log p\)

Step by step solution

01

Identify the logarithm property to be used

In this exercise, we have the logarithm of a power, \(\log p^8\). We'll use the property \(\log a^b = b \log a\) to express this as the sum or difference of logarithms.
02

Apply the logarithm property

Using the logarithm property, we rewrite the given expression as follows: \(\log p^8 = 8 \log p\)
03

Simplify the expression

In this case, the expression is already simplified. Therefore, the final result is: \(\log p^8 = 8 \log p\)

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Most popular questions from this chapter

Use the formula \(A=P e^{r t}\). Marisol wants to invest \(\$ 12,000\) now so that it grows to \(\$ 20,000\) in 7 yr. What interest rate should she look for? (Round to the nearest tenth of a percent.)

Write as a single logarithm. Assume the variables are defined so that the variable expressions are positive and so that the bases are positive real numbers not equal to \(1 .\) $$4 \log _{3} t-2 \log _{3} 6-2 \log _{3} u$$

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

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

Solve equation. \(\log _{4} k+\log _{4}(k-6)=2\)
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