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30 Logarithm Problems : Change of Base, Graphing and Solving for X

Find the exact values:

1) log (base 10) 1000
2) ln e^-100
3) log (base 5) (1/25)
4) log (base10) (0.1)
5) log (base 12) 3 + log (base 12) 48
6) 2^(log(base 2) 3 + log(base 2) 5)
7) e^(ln 15)
8) e^(3ln2)
9) log(base 8)320 - log(base8)5

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Use the properties of logarithms to expand the quantity.

1) LOG(BASE2)[( x^3 times y)/(z^2)]
2) ln(uv)^10
3) ln[(3x^2)/(x+1)^5]

Express the quantity as a single algorithm

1) log(base10)a - log(base10)b + log(base10)c
2) ln x + a ln y- b ln z
3) ½ ln x- 5 ln(x^2 +1)
4) Ln(x+y) + ln(x-y) -2lnz

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Evaluate using change of base formula:

a) log(base12)e
b) log(base6) 13.54
c) log(base2) pi
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Graph the functions and how are they related?
1) y=log(base2)x, y=log(base4)x, y=log(base6)x, y=log(base8)x
2) y=log(base1.5)x, y=lnx, y=log(base10)x, y=log(base50)x

Make a rough sketch of each function:

1) y=log(base10)(x+5)
2) y=-lnx
3) y=5+ln(x-2)

Solve each for x:

1) 2lnx=1
2) e^-x=5
3) e^(2x+3) - 7=0
4) 5^(x-3) =10
5) e^(3x+1)=k
6) ln(lnx)=1
7) 2lnx=ln2+ln(3x-4)
8) ln(5-2x)=-3
9) log(base10)(x+1)=4
10) e^e^x=10

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Thirty logarithm problems are solved. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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