SOLUTION: Please help me with these 4 problems somebody. thankyou!! 85. Write the expression of a single logarithm whose coefficient is 1 3lnx-1/3lny 87. express as a single logar

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Question 247745: Please help me with these 4 problems somebody. thankyou!!

85. Write the expression of a single logarithm whose coefficient is 1
3lnx-1/3lny
87. express as a single logarithmic quantity
1/2lnx+lny-2lnz
92. solve for x : ln2x - ln(X+5)=0
100. Cholestorol intake should be limited to 300mg or less each day. one serving of scrambled eggs from mcdonalds one double beef whopper from burger king exceed this intake by 241 mg. two servings of scrambled eggs and three double beef whoppers provide 1257 mg of cholesterol. determine the cholesterol content in each item
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Write the expression of a single logarithm whose coefficient is 1
3lnx-1/3lny
---
3*ln(x) - (1/3)*ln(y)
= ln(x^3) - ln(y^(1/3))
= ln[x^3/y^(1/3)]
-------------------------------
87. express as a single logarithmic quantity
(1/2)ln(x) + ln(y)- 2*ln(z)
-----------
ln(x^(1/2) + ln(y) - ln(z^2)
-----
ln[x^(1/2)*y/z^2]
============================

92. solve for x : ln(2x) - ln(X+5) = 0
ln[2x/(x+5)] 0
---
[2x/(x+5)] = e^0
2x = x+5
x = 5
=================

100. Cholestorol intake should be limited to 300 mg or less each day. One serving of scrambled eggs from mcdonalds one double beef whopper from burger king exceed this intake by 241 mg. Two servings of scrambled eggs and three double beef whoppers provide 1257 mg of cholesterol. determine the cholesterol content in each item.
---
e + w = 300+241
2e+3w = 1257
----------------------
e + w = 541
2e+3w = 1257
--------------------
2e + 2w = 1082
2e + 3w = 1257
---------------------
w = 175 mg (cholestorol in a whopper)
---
Substitute into e + w = 541 to solve for "e":
e + 175 = 541
e = 366 mg (cholestorol in scrambled eggs)
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Cheers,
Stan H.