# What is the solution of the equation log15 [1/(3^x + x - 5)]=x*(log15 5 - 1) ?

We have to solve log(15) [1/(3^x + x - 5)] = x * (log(15) 5 - 1).

log(15) [1/(3^x + x - 5)] = x * (log(15) 5 - 1)

=> log(15) [1/(3^x + x - 5)] = x*log(15) 5 - x

=> log(15) [1/(3^x + x - 5)] = x*log(15) 5 - log (15) 15^x

=> log(15) [1/(3^x + x - 5)] = log(15) (5^x/ 15^x)

=> [1/(3^x + x - 5)] = 5^x/ 15^x

=> [1/(3^x + x - 5)] = 1/ 3^x

=> 3^x = 3^x + x - 5

=> x - 5 = 0

=> x = 5

We get x = 5

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The passage contains a detailed solution to a logarithmic equation, including the steps taken to solve it and the final answer.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
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# What is the solution of the equation log15 [1/(3^x + x - 5)]=x*(log15 5 - 1) ?

We have to solve log(15) [1/(3^x + x - 5)] = x * (log(15) 5 - 1).

log(15) [1/(3^x + x - 5)] = x * (log(15) 5 - 1)

=> log(15) [1/(3^x + x - 5)] = x*log(15) 5 - x

=> log(15) [1/(3^x + x - 5)] = x*log(15) 5 - log (15) 15^x

=> log(15) [1/(3^x + x - 5)] = log(15) (5^x/ 15^x)

=> [1/(3^x + x - 5)] = 5^x/ 15^x

=> [1/(3^x + x - 5)] = 1/ 3^x

=> 3^x = 3^x + x - 5

=> x - 5 = 0

=> x = 5

We get x = 5

Approved by eNotes Editorial Team

Posted on
user
The passage contains a detailed solution to a logarithmic equation, including the steps taken to solve it and the final answer.

TYPE: SINGLE_QUESTION_WITH_ANSWER