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Chapter 13: Problem 38

Write as the sum or difference of logarithms and simplify, if possible. Assume all variables represent positive real numbers. $$\log _{4} \frac{s^{4}}{t^{6}}$$

Short Answer

Expert verified
The short answer is: \(\log_{4} \frac{s^{4}}{t^{6}} = 4\log_{4}(s) - 6\log_{4}(t)\)

Step by step solution

01

Apply the Quotient Rule

Since the given expression is a fraction, we can rewrite it as the difference of two logarithms using the quotient rule. \( \log _{4} \frac{s^{4}}{t^{6}} = \log_{4}(s^4) - \log_{4}(t^6) \)
02

Apply the Power Rule

Next, let's apply the power rule to both terms in the expression. \( \log_{4}(s^4) - \log_{4}(t^6) = 4\log_{4}(s) - 6\log_{4}(t) \) So, the given logarithmic expression can be written as the sum or difference of logarithms: $$\log _{4} \frac{s^{4}}{t^{6}} = 4\log_{4}(s) - 6\log_{4}(t)$$

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Most popular questions from this chapter

Use the formula \(A=P e^{r t}\). Cynthia wants to invest some money now so that she will have \(\$ 5000\) in the account in 10 yr. How much should she invest in an account earning \(8 \%\) compounded continuously?

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Use the formula \(A=P\left(1+\frac{r}{n}\right)^{n t}\) to solve each problem. How much will Anna owe at the end of 4 yr if she borrows \(\$ 5000\) at a rate of \(7.2 \%\) compounded weekly?
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