Long question! All written below.

Question

Part 1 [2 points] Is the following equation true?

Part 2 [6 points] Use complete sentences to explain the properties used in making your decision.

2 log 5 x + one-half log 5 y - 4 log 5 z = log 5x-squared times square root of y all over z to the fourth power.

Answer 1

Part 1

 

Lets get the right sides equal to the left side.

 

 

2log5x + (1/2)log5y - 4log5z = log((5x² √(y)) / z⁴)

 

2log5x + (1/2)log5y - 4log5z = log5x² + log√(y) - log z⁴

 

2log5x + (1/2)log5y - 4log5z = log5x² + log(y)^1/2 - log z⁴

 

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.