Answer:
x = 0.3125
Explanation:
You want the solution to the equation ...
log₂(5x) = log₂(x²) +4
Solution
Expanding the log expressions, we have ...
log₂(5) +log₂(x) = 2·log₂(x) +4
log₂(5) -4 = log₂(x) . . . . . . . subtract log₂(x)+4
log₂(x) -log₂(2⁴) = log₂(x)
Taking antilogs, this is ...
5/2⁴ = x
x = 5/16
x = 0.3125
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Additional comment
The log relations of interest are ...
log(a^b) = b·log(a)
log(a/b) = log(a) -log(b)
log₂(2^a) = a
Considering this last, it can be helpful to remember "a logarithm is an exponent."
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