Explanation Given information: The equation, log 2 x + log 2 ( x − 15 ) = 4 Concept used: The equivalent exponential form of a logarithm for a > 0 , x > 0 , a ≠ 1 is given by log b x = y if and only if x = b y Exponent property of Equality : If the same bases raised to different exponents are equal to each other, then their exponents will be equal as well. That is, if a m = a n then m = n Exponent property, 1 a n = a − n Product property of logarithm: log b m + log b n = log b ( m ⋅ n ) Calculation: To solve the given logarithmic equation, first write the left side of equation by using the product rule of logarithm as shown log 2 x + log 2 ( x − 15 ) = 4 log 2 [ x ( x − 15 ) ] = 4 Now, write it in equivalent exponential formusing the logarithmic to exponential conversion property that log b x = y if and only if x = b y

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 2, Problem 17SP

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Solve the given equation log2x+log2(x−15)=4 for x.

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٣:٥٣ النموذج الاول . . . O O O بشما ند الحمر الحمر الجمهورية الجنية وزارة التربية والتعليم اليوم التاريخ اللجنة العليا للاختبارات الزمن اختبار مادة الجبر والهندسة لجنة المطابع السرية المركزية للشهادة الثانوية العامة (القسم العلمي) الفترة %97 (1) ظلل في ورقة الإجابة الدائرة التي تحتوي على الحرف ( ص ) للإجابة الصحيحة والحرف ( خ ) للإجابة الخطأ بحسب رقم الفقرة لكل مما يأتي ( درجة لكل فقرة ) )1 ) 2 ) 3 ) 4 ) بؤرة القطع س" = ١٢ ص هي ( ۲ ) طول المحور الأصغر للقطع ٩ س + ص = ٩ يساوي 6 وحدات طول . ) إذا كان & عدد مركب ، 181 + 11 = ٦ ، فإن ١١ = ٣ . ) إذا كان م + ۳ ت = ۲ + ت ب م ، ب دع ، فإن م + ب = 5 ( ) إذا كان & = ۱ + ٣ ت ، فإن ٠ = ١٠ . 6 ( - ) إذا كان ٥٠ - ٣ - ١٢٠ ٤ - ٣ ، فإن قيمة ٧ = ٥ . 1 ) = N ) إذا كان ح هو الحد الخالي من س في المفكوك ( س + v. N 8 ( ( قيمة المقدار , = + ۱ ، * . . + ، فإن قيمة ٧ = ١٦ . ۱ + 9 ( ) المستقيمان المقاربان للقطع الذي معادلته س" = ١ هما ص = : ۹ 10 ( ) إذا كان ٥ + س = ٢٤ ، فإن قيمة س = - 1 س 11 ( ) إذا كانت النسبة بين الحدين الأوسطين تساوي 9 في المفكوك ( س + - ) ،…

Chapter 2 Solutions

Calculus

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Solve the given equation log 2 x + log 2 ( x − 15 ) = 4 for x.

Solution Summary: The author explains that if the same bases raised to different exponents are equal to each other, they will be equal as well.

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Solve the given equation log2x+log2(x−15)=4 for x.

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Chapter 2 Solutions