SOLUTION: Write the expression in terms of simpler logarithmic forms. ln x^4y^2/z^1/2

Algebra.Com
Question 368653: Write the expression in terms of simpler logarithmic forms.
ln x^4y^2/z^1/2

Answer by jsmallt9(3758)   (Show Source): You can put this solution on YOUR website!

There are three properties of logarithms which can be used to manipulate them:
Since the argument of your logarithm is a division/fraction, we will use the second property to split it into two logarithms:

The argument of the first logarithm is a product so we will use the first property to split it into two logarithms:

The arguments all three logarithms have an exponent. We can use the third property on them to move the argument out in front:

By using the properties as we have, the expression as a whole is more complex but the arguments of the logarithms are now just a simple variable.

RELATED QUESTIONS

Write problem in terms of simpler logarithmic forms log b v^7/... (answered by rapaljer)
use properties of logarithms to condense the logarithmic expression below 3 ln X+2 ln... (answered by solver91311)
Write the expression as the logarithm of a single quantity. 1/2 ln x+ 2 ln y- 3 ln z (answered by Alan3354)
Write the following expression as a single logarithm:1/2 ln x - ln y + ln zł (answered by lwsshak3)
Hi guys i need some help with this question. expand the quantity as sum and... (answered by ankor@dixie-net.com)
Use properties of logarithms to condense the logarithmic expression. Write the expression (answered by Theo)
Expand the logarithmic expression of... (answered by ankor@dixie-net.com)
write 1/2[lnx+ln(x+2)]-2ln(x-5)as a single logarithmic... (answered by jsmallt9)
Assume that x, y, and z are positive numbers. Use the properties of logarithms to write... (answered by Fombitz)