The Logarithm Function. The Exponential Function & Arbitrary Powers: Other BasesPart-1(a)-...

Question

The Logarithm Function. The Exponential Function & Arbitrary Powers: Other Bases
Part-1(a)- Part-2(d)
calculus
1. (1 pt) Find the exact value of each expression.
(a) logs 2 (b) lneVI (a) (b) Correct Answers: • 0.333333333333333 • 1.4142135623731
2. (1 pt) Find the exact value of each expression.
(a) log 1.25 + log 8 (b) log5 10 + 1og5 20 — 31og5 2 (a) (b) Correct Answers:
• 2
• 2
3. (1 pt) Express the given quantity as a single logarithm.
lnx+21ny-71nz
Correct Answers: • ln(x*y^{2}/ z"{7})
4. (1 pt) Find the exact value of each expression.
(a) 21c12 3+log2 5 (b) e3 m2 (a) (b) Correct Answers:
• 15
• 8
5. (1 pt) Select True or False for each statement.
You must get all of the answers correct to receive credit.
ln(3ab) = bln a +1n3
In ?Ay = 3(lnx + lny) 1og2 4 = logs 8 + .5 log416 (lna)3b = 3blna Correct Answers:
• True • True • True • False
6. (1 pt) The expression 35x-134-2x can be written as 31(4, where f(x) is a function of x. Find . = Correct Answers: • (5 - 2)*x + (4 -1)
7. (1 pt) The expression (2-4)5x can be written as 21(4, where f(x) is a function of x. Find f . f = Correct Answers: • (-4)*(5)*x
8. (1 pt) Suppose that f = (8 — 2x)?. (A) List all the critical values of f(x). Note: If there are no critical values, enter 'NONE'.
(B) Use interval notation to indicate where f(x) is increas-ing. Note: Use '114F' for co, '-INF' for —co, and use 'U' for the union symbol. Increasing. (C) Use interval notation to indicate where f (4 is decreas-ing. Decreasing. (D) List the x values of all local maxima of f . If there are no local maxima, enter 'NONE'. x values of local maximums = (E) List the x values of all local minima of f . If there are no local minima, enter 'NONE'. x values of local minimums = (F) Use interval notation to indicate where f(x) is concave up. Concave up. (G) Use interval notation to indicate where f(x) is concave down. Concave down. (H) List the x values of all the inflection points of f . If there are no inflection points, enter 'NONE'. x values of inflection points =

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David · Accepted Answer

1) 
Exact value of a) log82= log88
1/3=1/3=0.3333.. 
b) lne√2=√2lne=√2=1.414 
2)a. log1.25+log8=log10=1 
b.log510+ log520- 3log52= log5200/8= log525=2 
3) lnx+2lny-7lnz=ln(x*y2/z7) 
4) 2log2
3+ log
2
5=2 log2
15=15 
  e3ln2=eln8=8 
5) a True 
b.  True 
c. True 
d.False because its power to whole expression 
6) f(x)=5x-1+4-2x=3x+3 
7)f(x)=-4*5x=-20x 
8) f(x)=(8-2x)exp(x) 
a) f’(x)= (8-2x)exp(x)-2exp(x)=0 which gives x=3 
b) f(x) increasing i.e f’(x) >0 i.e  (-INF , 3] 
c) f(x) is decreasing i.e f’(x) f(x) is concave up for all values of (-INF, 2) 
g) f”(x)= (8-2x)exp(x)--4exp(x) >0 for all x>2  => f(x) is concave down for all values of (2, INF) 
h) at x=2 ,f”(x)=0 
i)
9)f(x)=ln(x^4+432) 
a. f’(x)=4x^3/(x^4+432)> for all x>0 => increasing function on (0 inf) 
b. f’(x)  no local maxima 
d. no local minima same reasoning as above 
e. f”(x)=( 432*12*x^2-4*x^6)/(x^4+432)^20  => R-(-6 6)
10.  a)  x=5+log72=5.357 
b) lnx+ln(x-1)=1 => x^2-x-e => x=0.5+0.5sqrt(1+4e) 
11.

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The Logarithm Function. The Exponential Function & Arbitrary Powers: Other Bases Part-1(a)- Part-2(d) calculus 1. (1 pt) Find the exact value of each expression. (a) logs 2 (b) lneVI (a) (b) Correct...

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