Question

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

Answer 1

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.