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How to solve 12??????

How to solve 12??????-example-1

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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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User Amirshk
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