+0

# help with algebra!! (logs)

0
49
2

Find a/b when 2log(a-2b) = log(a) + log(b).

Mar 22, 2021

#1
+23
+1

2 log (a - 2b  )  = loga + log b

log (a - 2b)^2  = log (a*b)

This implies that

(a - 2b)^2  =  ab

a^2 - 4ab + 4b^2  = ab

a^2 - 5ab + 4b^2  = 0

(a - 4b) (a - b)  = 0

This implies that

a = 4b   ⇒   a/b  =  4      or

a - b  = 0  ⇒   a  = b  ⇒   a/b  =  1

Mar 22, 2021
#2
+23
0

Hope this helps, feel free to tell me if i'm wrong :)

Mar 22, 2021
The text contains a mathematical question involving logarithms and a detailed solution that provides two possible answers for the ratio a/b.
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
system
+0

# help with algebra!! (logs)

0
49
2

Find a/b when 2log(a-2b) = log(a) + log(b).

Mar 22, 2021

#1
+23
+1

2 log (a - 2b  )  = loga + log b

log (a - 2b)^2  = log (a*b)

This implies that

(a - 2b)^2  =  ab

a^2 - 4ab + 4b^2  = ab

a^2 - 5ab + 4b^2  = 0

(a - 4b) (a - b)  = 0

This implies that

a = 4b   ⇒   a/b  =  4      or

a - b  = 0  ⇒   a  = b  ⇒   a/b  =  1

Mar 22, 2021
#2
+23
0

Hope this helps, feel free to tell me if i'm wrong :)

Mar 22, 2021
user
The text contains a mathematical question involving logarithms and a detailed solution that provides two possible answers for the ratio a/b.

TYPE: SINGLE_QUESTION_WITH_ANSWER