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 To solve the equation: log\u20612(3x\u22127)=3\\log_2(3x – 7) = 3<\/p>\n\n\n\n This is a logarithmic equation with base 2. It says: log\u20612(3x\u22127)=3\\log_2(3x – 7) = 3<\/p>\n\n\n\n This means: 3x\u22127=233x – 7 = 2^3<\/p>\n\n\n\n 23=82^3 = 8<\/p>\n\n\n\n Now the equation becomes: 3x\u22127=83x – 7 = 8<\/p>\n\n\n\n Add 7 to both sides: 3x=153x = 15<\/p>\n\n\n\n Now divide both sides by 3: x=5x = 5<\/p>\n\n\n\n 5\\boxed{5}<\/p>\n\n\n\n This equation involves a logarithm with base 2. A logarithmic equation such as log\u2061b(A)=C\\log_b(A) = C is equivalent to an exponential form: A=bCA = b^C. This is the key idea for solving logarithmic equations.<\/p>\n\n\n\n In the given equation, log\u20612(3x\u22127)=3\\log_2(3x – 7) = 3, the expression inside the logarithm is 3x\u221273x – 7, the base is 2, and the result is 3. Rewriting it in exponential form gives us: 3x\u22127=233x – 7 = 2^3<\/p>\n\n\n\n Calculating 232^3 gives 8, so we simplify: 3x\u22127=83x – 7 = 8<\/p>\n\n\n\n This is a basic linear equation. We solve it by first isolating 3x3x through addition: 3x=153x = 15<\/p>\n\n\n\n Then, divide both sides by 3: x=5x = 5<\/p>\n\n\n\n However, when solving logarithmic equations, it\u2019s essential to check if the solution is valid<\/strong>. Logarithms are only defined for positive<\/strong> arguments. That means: 3x\u22127>0\u21d2x>733x – 7 > 0 \\Rightarrow x > \\frac{7}{3}<\/p>\n\n\n\n Our solution, x=5x = 5, satisfies this condition, so it is valid.<\/p>\n\n\n\n Therefore, the only correct solution is: 5\\boxed{5}<\/p>\n","protected":false},"excerpt":{"rendered":" What is the solution of log2 (3x – 7) = 3? The correct answer and explanation is: To solve the equation: log\u20612(3x\u22127)=3\\log_2(3x – 7) = 3 Step-by-Step Solution: Step 1: Understand what the equation means. This is a logarithmic equation with base 2. It says: log\u20612(3x\u22127)=3\\log_2(3x – 7) = 3 This means: 3x\u22127=233x – 7 […]<\/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-17476","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/17476","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=17476"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/17476\/revisions"}],"predecessor-version":[{"id":17477,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/17476\/revisions\/17477"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=17476"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=17476"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=17476"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step-by-Step Solution:<\/h3>\n\n\n\n
Step 1: Understand what the equation means.<\/h4>\n\n\n\n
Step 2: Calculate 232^3<\/h4>\n\n\n\n
Step 3: Solve for xx<\/h4>\n\n\n\n
Final Answer:<\/h3>\n\n\n\n
\n\n\n\nExplanation (Approx. 300 Words):<\/h3>\n\n\n\n