Michael J. answered • 03/10/15

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**Part 1**

Lets get the right sides equal to the left side.

2log5x + (1/2)log5y - 4log5z = log

**(**(5x^{2}√(y)) / z^{4}**)**2log5x + (1/2)log5y - 4log5z = log5x

^{2}+ log√(y) - log z^{4}2log5x + (1/2)log5y - 4log5z = log5x

^{2}+ log(y)^{1/2}- log z^{4}2log5x + (1/2)log5y - 4log5z = 2log5x + (1/2)log y - 4log z

The equation is not true.

**Part 2**

First, I wrote the right side as a sum and difference of logs. I do this by logging each term separated by an operator. Secondly, I transformed the √ into the exponent of 1/2. This way, every term on the right side has exponents. Lastly, I brought down the exponents as the coefficients of the log terms.

The 2nd and last terms on the left side does not equal the 2nd and last terms on the right side.