Logarithms and Simultaneous Equations
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1. Given that x and y are both positive, solve the simultaneous equations
log(xy) =7
log(x/y) =1
Answers given: x = 10000
y = 1000
2. log (p - q +1) =0
log (pq) + 1 = 0
Show that p = q = 1/square root 10
3. Solve the following equation for x:
2^2x + 1 - 9 x 2^x + 4 = 0
Answer given: -1, 2
4. Example of exam question
Solve the pair of simultaneous equations
log(x + y) = 0
2 log x = log (y - 1)
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Logarithms and simultaneous equations are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.
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I assume you are familiar with the log laws and definition of log (see appendix)
Questions 1 and 2 are in the attachments, it was easier to just scan them.
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Q3. Solve the following equation for x:
2^(2x + 1) - 9 x 2^x + 4 = 0 (this was sloppy, you must use brackets to be clear.)
Answer given: -1, 2
SOLUTION: This is a quadratic in 2^x.
2 (2^x)^2 - 9 (2^x) +4 = 0
Factorise to get
( 2(2^x) - 1 )( 2^x - 4 ) = 0
2(2^x) - 1 = 0 or 2^x - 4 = 0
2(2^x) = 1 or 2^x = 4
2^x = 1/2 ...
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