Question

Part 2 - Find the error(s) and solve the problem correctly.

Answer 1

The problem solved correctly as a single logarithm is $log_{a} 2x^{3}/y^{2}$

Simplifying Logarithm

From the question, we are to simplify the given logarithm

The given logarithm is

$log_{a} 2x \ + \ 2(log_{a} x -log_{a} y)$

From the subtraction law of logarithm, we have that

$log_{c} a -log_{c} b = log_{c} (a/b)$

Thus,

The error in the solution was instead of multiplying, a was supposed to be divided by b

The correct solution is

$log_{a} 2x \ + \ 2(log_{a} x -log_{a} y)$

$log_{a} 2x \ + \ 2(log_{a} (x/y) )$

$log_{a} 2x \ + \ log_{a} (x/y)^{2}$

$log_{a} 2x \ + \ log_{a} (x^{2}/y^{2})$

Simplifying further

$log_{a} 2x \times (x^{2}/y^{2})$

$log_{a} 2x \times x^{2}/y^{2}$

$log_{a} 2x^{3}/y^{2}$

Hence, the problem solved correctly as a single logarithm is $log_{a} 2x^{3}/y^{2}$

Learn more on Simplifying logarithms here: brainly.com/question/247340

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