Respuesta :
The solution to maria’s equation [tex]\rm log\frac{x}{2} +log\frac{20}{x^{2} } = log8[/tex] by using the properties of the logarithm is 5/4.
What is a logarithm?
A logarithm is the exponentiation inverse function that can be expressed by the exponent or power to which a base must be raised to yield a number.
It is given that
[tex]\rm log\frac{x}{2} +log\frac{20}{x^{2} } = log8[/tex]
Using properties of a logarithm, we get
[tex]\rm log x + log y=logxy[/tex]
[tex]\rm log[\frac{x}{2} \times\frac{20}{x^{2} }] = log8\\\rm log[\frac{10}{x}] = log8[/tex]
on comparing
10/x = 8
x = 10/8
x = 5/4
Hence, the solution to maria’s equation [tex]\rm log\frac{x}{2} +log\frac{20}{x^{2} } = log8[/tex] is 5/4.
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