/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 15 Write as the sum or difference o... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

Write as the sum or difference of logarithms and simplify, if possible. Assume all variables represent positive real numbers. $$\log _{5} 2^{3}$$

Short Answer

Expert verified
The simplified expression is \(\log _{5} 2^{3} = 3\log_{5} 2\).

Step by step solution

01

Use the power rule for logarithms

The power rule states that \(\log_{a} (x^{n}) = n\cdot \log_{a} (x)\). Using this rule, rewrite the expression: \(\log _{5} 2^{3} = 3\log_{5} 2\) No other properties of logarithms can be applied to the given expression, as our final expression only contains one logarithm term. So, the simplified expression is:
02

Final Answer

\(\log _{5} 2^{3} = 3\log_{5} 2\)

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Study anywhere. Anytime. Across all devices.