Unit 1 Test
1 answer:
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1/3 ln(<em>x</em>) + ln(2) - ln(3) = 3
Recall that , so
ln(<em>x</em> ¹ʹ³) + ln(2) - ln(3) = 3
Condense the left side by using sum and difference properties of logarithms:
Then
ln(2/3 <em>x</em> ¹ʹ³) = 3
Take the exponential of both sides; that is, write both sides as powers of the constant <em>e</em>. (I'm using exp(<em>x</em>) = <em>e</em> ˣ so I can write it all in one line.)
exp(ln(2/3 <em>x</em> ¹ʹ³)) = exp(3)
Now exp(ln(<em>x</em>)) = <em>x </em>for all <em>x</em>, so this simplifies to
2/3 <em>x</em> ¹ʹ³ = exp(3)
Now solve for <em>x</em>. Multiply both sides by 3/2 :
3/2 × 2/3 <em>x</em> ¹ʹ³ = 3/2 exp(3)
<em>x</em> ¹ʹ³ = 3/2 exp(3)
Raise both sides to the power of 3:
(<em>x</em> ¹ʹ³)³ = (3/2 exp(3))³
<em>x</em> = 3³/2³ exp(3×3)
<em>x</em> = 27/8 exp(9)
which is the same as
<em>x</em> = 27/8 <em>e</em> ⁹
Given that a certain antihistamine is often prescribed for allergies.
And typical dose for 100-pound person is 25 mg every 6 hours.
a) Let us calculate dose per 1 hour for 100-pound person=
Since 1 week means 7X24= 168 hours, dosage per 1 week = dosage per 168 hours
The number of 12.8 chew able tablets would be taken in a week=
Hence number of 12.8mg chew able tablets would be taken in a week is 55.
b) Now we can use earlier answer for this problem, since 12.8mg tablet is replaced with 9ml liquid, 55 bottles of 9ml liquid are to be taken in a week.
Hence amount of liquid histamine should a 100-pound person take in a week = 55X9
=495ml