The problem solved correctly as a single logarithm is [tex]log_{a} 2x^{3}/y^{2}[/tex]
From the question, we are to simplify the given logarithm
The given logarithm is
[tex]log_{a} 2x \ + \ 2(log_{a} x -log_{a} y)[/tex]
From the subtraction law of logarithm, we have that
[tex]log_{c} a -log_{c} b = log_{c} (a/b)[/tex]
Thus,
The error in the solution was instead of multiplying, a was supposed to be divided by b
The correct solution is
[tex]log_{a} 2x \ + \ 2(log_{a} x -log_{a} y)[/tex]
[tex]log_{a} 2x \ + \ 2(log_{a} (x/y) )[/tex]
[tex]log_{a} 2x \ + \ log_{a} (x/y)^{2}[/tex]
[tex]log_{a} 2x \ + \ log_{a} (x^{2}/y^{2})[/tex]
Simplifying further
[tex]log_{a} 2x \times (x^{2}/y^{2})[/tex]
[tex]log_{a} 2x \times x^{2}/y^{2}[/tex]
[tex]log_{a} 2x^{3}/y^{2}[/tex]
Hence, the problem solved correctly as a single logarithm is [tex]log_{a} 2x^{3}/y^{2}[/tex]
Learn more on Simplifying logarithms here: https://brainly.com/question/247340
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