What is the solution of log2 (3x – 7) = 3?<\/p>\n\n\n\n
The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n The solution to the equation log\u2082(3x \u2212 7) = 3<\/strong> is: We are given the logarithmic equation: log\u20612(3x\u22127)=3\\log_2(3x – 7) = 3<\/p>\n\n\n\n This means: log\u2061b(A)=C\u21d2A=bC\\log_b(A) = C \\quad \\Rightarrow \\quad A = b^C<\/p>\n\n\n\n So: 3x\u22127=233x – 7 = 2^3 3x\u22127=83x – 7 = 8<\/p>\n\n\n\n 3x=8+7=153x = 8 + 7 = 15 x=153=5x = \\frac{15}{3} = 5<\/p>\n\n\n\n Substitute x=5x = 5 into the original equation: log\u20612(3(5)\u22127)=log\u20612(15\u22127)=log\u20612(8)\\log_2(3(5) – 7) = \\log_2(15 – 7) = \\log_2(8) log\u20612(8)=3(because 23=8)\\log_2(8) = 3 \\quad \\text{(because } 2^3 = 8\\text{)}<\/p>\n\n\n\n \u2705 This confirms the solution is correct.<\/p>\n\n\n\n For any logarithmic expression like log\u2061b(A)\\log_b(A), the argument A must be positive<\/strong>.<\/p>\n\n\n\n In our case, 3x\u22127>03x – 7 > 0 3x>7\u21d2x>733x > 7 \\Rightarrow x > \\frac{7}{3}<\/p>\n\n\n\n Since x=5x = 5 is greater than 73\\frac{7}{3}, it lies within the valid domain.<\/p>\n\n\n\n x=5\\boxed{x = 5}<\/p>\n\n\n\n This means when you plug 5 into the expression, the logarithmic identity is satisfied.<\/p>\n","protected":false},"excerpt":{"rendered":" What is the solution of log2 (3x – 7) = 3? The correct answer and explanation is: \u2705 Correct Answer: The solution to the equation log\u2082(3x \u2212 7) = 3 is:x = 5 \ud83e\udde0 Step-by-Step Explanation: We are given the logarithmic equation: log\u20612(3x\u22127)=3\\log_2(3x – 7) = 3 This means:“The power to which 2 must be […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-23327","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/23327","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=23327"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/23327\/revisions"}],"predecessor-version":[{"id":23328,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/23327\/revisions\/23328"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=23327"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=23327"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=23327"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}\u2705 Correct Answer:<\/h3>\n\n\n\n
x = 5<\/strong><\/p>\n\n\n\n
\n\n\n\n\ud83e\udde0 Step-by-Step Explanation:<\/h3>\n\n\n\n
“The power to which 2 must be raised to get (3x \u2212 7) is 3.”<\/strong><\/p>\n\n\n\n
\n\n\n\n\ud83d\udd01 Step 1: Convert the logarithmic equation to exponential form<\/h3>\n\n\n\n
\n\n\n\n\u270f\ufe0f Step 2: Solve the linear equation<\/h3>\n\n\n\n
\n\n\n\n\u2705 Step 3: Check the solution<\/h3>\n\n\n\n
\n\n\n\n\u26a0\ufe0f Important Note on Domain:<\/h3>\n\n\n\n
\n\n\n\n\ud83d\udccc Final Answer:<\/h3>\n\n\n\n