Which of the following expressions is not equal to log(5^2 / 3) ? Explain. a) (2)/(3) log(5) b)

Name: Problem 100, Chapter 11: Algebra for College Students
Uploaded: 2020-04-13T00:44:54-08:00
Duration: 1 min 35 s
Channel: Heather Zimmers
Description: Which of the following expressions is not equal to log(5^2 / 3) ? Explain. a) (2)/(3) log(5) b) (log(5)+log(5))/(3) c) (log(5))^2 / 3 d) (1)/(3) log(25)

step 1 All right, three of these answer choices are equal to the log of 5 to the 2 thirds, and one of t

Question

Which of the following expressions is not equal to $\log \left(5^{2 / 3}\right) ?$ Explain. a) $\frac{2}{3} \log (5)$ b) $\frac{\log (5)+\log (5)}{3}$ c) $(\log (5))^{2 / 3}$ d) $\frac{1}{3} \log (25)$

   Which of the following expressions is not equal to $\log \left(5^{2 / 3}\right) ?$ Explain.
a) $\frac{2}{3} \log (5)$
b) $\frac{\log (5)+\log (5)}{3}$
c) $(\log (5))^{2 / 3}$
d) $\frac{1}{3} \log (25)$

Algebra for College Students

Mark Dugopolski 5th Edition

Chapter 11, Problem 100

Instant Answer

Solved by Expert Heather Zimmers

04/13/2020

Step 1

Using the power rule of logarithms, which states that $\log_b a^n = n \log_b a$, we can rewrite this as $\log \left(5^{2 / 3}\right)$. Therefore, option a) is equivalent to the original expression. Show more…

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Which of the following expressions is not equal to $\log \left(5^{2 / 3}\right) ?$ Explain. a) $\frac{2}{3} \log (5)$ b) $\frac{\log (5)+\log (5)}{3}$ c) $(\log (5))^{2 / 3}$ d) $\frac{1}{3} \log (25)$

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Key Concepts

Properties of Logarithms

Logarithms have several key properties that simplify the manipulation of expressions. One of the most important is the power rule, which states that log(a^b) is equal to b * log(a). This rule allows one to transform the logarithm of an exponentiated number into a product, making expressions easier to compare or simplify.

Distinguishing Exponentiation of Logarithms vs. the Logarithm of an Exponentiated Expression

It is important to recognize the difference between an expression where the logarithm itself is raised to a power, such as (log(a))^(b), and one where the power is applied to the argument of the logarithm, like log(a^(b)). The former does not follow the logarithmic power rule and generally yields a value different from simply multiplying the logarithm by the exponent, thereby making it not equivalent to the manipulated form using the power rule.

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