{"id":218014,"date":"2025-05-23T06:01:16","date_gmt":"2025-05-23T06:01:16","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=218014"},"modified":"2025-05-23T06:01:18","modified_gmt":"2025-05-23T06:01:18","slug":"use-a-luildi-17-log-10000-9-log2-64-10-log2-1024-11-log2-128-18-log-1000-19-log-v1000-12-log2-256-20-log-10000-13-log42-21-log","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/23\/use-a-luildi-17-log-10000-9-log2-64-10-log2-1024-11-log2-128-18-log-1000-19-log-v1000-12-log2-256-20-log-10000-13-log42-21-log\/","title":{"rendered":"use a LUILDI 17 log 10000 9 log2 64 10 log2 1024 11 log2 128 18 log 1000 19 log V1000 12 log2 256 20 log 10000 13 log42 21 log"},"content":{"rendered":"\n

JUJ Wu Luerlises. use a LUILDI 17 log 10000 9 log2 64 10 log2 1024 11 log2 128 18 log 1000 19 log V1000 12 log2 256 20 log 10000 13 log42 21 log, 83.1 14 log: 2 15 log48 16 log: 128 22 log, 26.3 23 log1632 24 log27 81<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Let’s first interpret your list of logarithmic expressions and then solve each one. Afterward, I’ll provide a detailed explanation of logarithmic principles to help clarify how each solution was reached.<\/p>\n\n\n\n

\n\n\n\n

Correct Answers:<\/h3>\n\n\n\n
    \n
  1. log 10000<\/strong> \u2192 4<\/strong><\/li>\n\n\n\n
  2. log\u2082 64<\/strong> \u2192 6<\/strong><\/li>\n\n\n\n
  3. log\u2082 1024<\/strong> \u2192 10<\/strong><\/li>\n\n\n\n
  4. log\u2082 128<\/strong> \u2192 7<\/strong><\/li>\n\n\n\n
  5. log 1000<\/strong> \u2192 3<\/strong><\/li>\n\n\n\n
  6. log \u221a1000<\/strong> \u2192 1.5<\/strong><\/li>\n\n\n\n
  7. log\u2082 256<\/strong> \u2192 8<\/strong><\/li>\n\n\n\n
  8. log 10000<\/strong> \u2192 4<\/strong><\/li>\n\n\n\n
  9. log\u2084 2<\/strong> \u2192 0.5<\/strong><\/li>\n\n\n\n
  10. log\u2082 2<\/strong> \u2192 1<\/strong><\/li>\n\n\n\n
  11. log\u2084 8<\/strong> \u2192 1.5<\/strong><\/li>\n\n\n\n
  12. log\u2084 128<\/strong> \u2192 3.5<\/strong> (approx.)<\/li>\n\n\n\n
  13. log\u2081\u2080 83.1<\/strong> \u2192 \u2248 1.919<\/strong><\/li>\n\n\n\n
  14. log\u2081\u2080 26.3<\/strong> \u2192 \u2248 1.420<\/strong><\/li>\n\n\n\n
  15. log\u2081\u2080 1632<\/strong> \u2192 \u2248 3.213<\/strong><\/li>\n\n\n\n
  16. log\u2082\u2087 81<\/strong> \u2192 4\/3 or \u2248 1.333<\/strong><\/li>\n<\/ol>\n\n\n\n
    \n\n\n\n

    <\/h3>\n\n\n\n

    Logarithms<\/strong> are the inverse operations of exponentiation. In simpler terms, a logarithm answers the question: “To what exponent must a given base be raised to produce a certain number?”<\/p>\n\n\n\n

    The notation log_b(x)<\/code> means “the power you raise b<\/strong> to get x<\/strong>.”<\/p>\n\n\n\n

    For example:<\/p>\n\n\n\n

      \n
    • log\u2081\u2080 1000 = 3<\/code> because $10^3 = 1000$<\/li>\n\n\n\n
    • log\u2082 64 = 6<\/code> because $2^6 = 64$<\/li>\n<\/ul>\n\n\n\n

      Here\u2019s how we evaluate these step-by-step:<\/p>\n\n\n\n

        \n
      1. log 10000<\/strong>: Base 10 is implied. $10^4 = 10000$, so answer is 4.<\/li>\n\n\n\n
      2. log\u2082 64<\/strong>: $2^6 = 64$, so the logarithm is 6.<\/li>\n\n\n\n
      3. log\u2082 1024<\/strong>: $2^{10} = 1024$, so it\u2019s 10.<\/li>\n\n\n\n
      4. log\u2082 128<\/strong>: $2^7 = 128$, so it\u2019s 7.<\/li>\n\n\n\n
      5. log 1000<\/strong>: $10^3 = 1000$, so it\u2019s 3.<\/li>\n\n\n\n
      6. log \u221a1000<\/strong>: $\\sqrt{1000} = 10^{1.5}$, so log is 1.5.<\/li>\n\n\n\n
      7. log\u2082 256<\/strong>: $2^8 = 256$, so it’s 8.<\/li>\n\n\n\n
      8. log\u2084 2<\/strong>: What power of 4 gives 2? Since $4^{0.5} = 2$, the answer is 0.5.<\/li>\n\n\n\n
      9. log\u2082 2<\/strong>: $2^1 = 2$, so it\u2019s 1.<\/li>\n\n\n\n
      10. log\u2084 8<\/strong>: Rewrite 8 as $2^3$ and 4 as $2^2$, so $log\u2084 8 = log\u2082 8 \/ log\u2082 4 = 3 \/ 2 = 1.5$<\/li>\n\n\n\n
      11. log\u2084 128<\/strong>: Use change of base: $\\log\u2084 128 = \\log_{10}128 \/ \\log_{10}4 \u2248 2.107 \/ 0.602 \u2248 3.5$<\/li>\n\n\n\n
      12. log\u2081\u2080 83.1<\/strong>: Use calculator: \u2248 1.919<\/li>\n\n\n\n
      13. log\u2081\u2080 26.3<\/strong>: Use calculator: \u2248 1.420<\/li>\n\n\n\n
      14. log\u2081\u2080 1632<\/strong>: Use calculator: \u2248 3.213<\/li>\n\n\n\n
      15. log\u2082\u2087 81<\/strong>: Since $27 = 3^3$ and $81 = 3^4$, then: $$
        \\log_{27}81 = \\frac{\\log_3 81}{\\log_3 27} = \\frac{4}{3} \u2248 1.333
        $$<\/li>\n<\/ol>\n\n\n\n
        \n\n\n\n

        Logarithms are essential in many fields, including science, engineering, and data analysis, because they simplify complex multiplications and exponential growth. They also form the basis of scales like the Richter and decibel scales.<\/p>\n\n\n\n

        \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

        JUJ Wu Luerlises. use a LUILDI 17 log 10000 9 log2 64 10 log2 1024 11 log2 128 18 log 1000 19 log V1000 12 log2 256 20 log 10000 13 log42 21 log, 83.1 14 log: 2 15 log48 16 log: 128 22 log, 26.3 23 log1632 24 log27 81 The Correct Answer and […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-218014","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/218014","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=218014"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/218014\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=218014"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=218014"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=218014"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}