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HELP ME PLEASE!! solve this logarithmic equation for the values of the variable. Be sure to check for extraneous solutions!! Thank you!

HELP ME PLEASE!! solve this logarithmic equation for the values of the variable. Be-example-1
User Mclaughj
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1 Answer

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Explanation:

log2(20) - log2(x) = log2(20/x)

log2(5) + log2(x) = log2(5x)

so, we have

log2(20/x) = log2(5x)

20/x = 5x

20 = 5x²

x² = 20/5 = 4

x = ±2

x = 2 makes all arguments for the log funding positive, and is therefore a valid solution.

x = -2 makes the arguments of some log functions negative (e.g. log2(x)). this is impossible, so, x = -2 is an extraneous solution.

User Teamchong
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