## College Algebra (6th Edition)

Published by Pearson

# Chapter 4 - Exponential and Logarithmic Functions - Exercise Set 4.3 - Page 477: 4

#### Answer

$1+log_{9}x$

#### Work Step by Step

Based on the product rule of logarithms, we know that $log_{b}(MN)=log_{b}M+log_{b}N$ (for $M\gt0$ and $N\gt0$). Therefore, $log_{9}(9x)=log_{9}9+log_{9}x$. Based on the definition of the logarithmic function, we know that $y=log_{b}x$ is equivalent to $b^{y}=x$ (for $x\gt0$ and $b\gt0$, $b\ne1$). Therefore, $log_{9}9=1$, because $9^{1}=9$. So, $log_{9}9+log_{9}x=1+log_{9}x$.

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.
{"ft_lang_label":"__label__en","ft_lang_prob":0.61230636,"math_prob":0.9935034,"size":416,"snap":"2019-13-2019-22","text_gpt3_token_len":181,"char_repetition_ratio":0.18446602,"word_repetition_ratio":0.0,"special_character_ratio":0.42548078,"punctuation_ratio":0.114285715,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99968386,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-05-20T17:14:02Z\",\"WARC-Record-ID\":\"<urn:uuid:0236422a-8e69-40c4-a2de-40252887de8c>\",\"Content-Length\":\"97227\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:6ce62895-be51-463f-b5b6-c860285304ce>\",\"WARC-Concurrent-To\":\"<urn:uuid:6279d3ae-38b8-43ab-b1f2-335bd90cb5df>\",\"WARC-IP-Address\":\"52.6.107.41\",\"WARC-Target-URI\":\"https://www.gradesaver.com/textbooks/math/algebra/college-algebra-6th-edition/chapter-4-exponential-and-logarithmic-functions-exercise-set-4-3-page-477/4\",\"WARC-Payload-Digest\":\"sha1:PVD4VCZATRSU4RRIA2BNLNV34EZQVDGW\",\"WARC-Block-Digest\":\"sha1:LH2TUI7XUAOGRNDLJ6ORRA2BAGERISHZ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-22/CC-MAIN-2019-22_segments_1558232256082.54_warc_CC-MAIN-20190520162024-20190520184024-00259.warc.gz\"}"}