Verify these answers please.

1. Which of the following functions would f(x) = log(base 10)x horizontally 4 units to the left?

a) f(x)=log(base10)(x-4)
b) f(x)=4Log(base10)X
c) f(x)=log(base10) x+4

Answer: C
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2. State the transformations, in proper order, that are needed to turn f(x) = -8log(base10)x+6 into f(x)=4log(base10)x+1

a) reflection about the x-axis, vertical compression by a factor of 1/2, vertical translation 5 units down.

b) reflection about the y-axis, vertical stretch by a factor of 2, vertical translation 5 units up.

c) vertical translation 5 units down, vertical compression by a factor of 1/2, reflection about the x-axis.

d) Reflection about the x-axis, vertical translation 5 units down, vertical compression by a factor of 1/2.

Answer: A

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3. Which of the values in general logarithmic function f(x)=alog(base10)(k(x-d)) + c should be multiplied by -1 in order to cause a reflection in the y-axis?

a) a
b) k
c) d
d) c

Answer A.
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4. Which of the following functions results if f(x) log(base 10)x is vertically stretched by a factor of 4, horizontally stretched by a factor of 3, reflected in the y-axis, horizontally translated 5 units to the right and vertically translated 2 units up?

a) f(x)= -4log(base10) [1/3(x-5)] + 2

b) f(x)= 4log(base10) [-1/3(x-5)] + 2

c) f(x)= 4log(base10) [-3(x-5)] + 2

d)f(x)= -4log(base10) [-1/3(x-5)] + 2

Answer: A
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5. Which is the first transformation that should be applied the graph of f(x) = log(base10)x to the graph f(x)=4log(base10)(x-5) + 3?

a) vertical stretch by a factor of 4
b) horizontal translation 5 units to the right
c) vertical translation 3 units up
d)vertical compression by a factor of 4

Answer:A
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6. A certain radioactive isotope has a half life of 5 years. If a sample has 120 grams of radioactive material, what equation could be used to determine the amount of material remaining (y) after x years.

a) y=120 x (1/2)^5x

b) y=60^5x

c) y=120x5^(1/2)^x

d) y=1/2x120^5x

Answer: A

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7. State the law of logarithms used to rewrite log(base 5)32 - log(base 5)8 as log(base 5)4.

a) difference of law of log
b) product law of log
c) power law
d) quotient law

Answer: D
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8. Which of the following log equations is undefined?

a) log(base -x)10=100
b) log(base x) - 10=100
c) log(base10)100=-x
d) log(base10)100=10^-x

ANswer: A
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1. To verify the answer for this question, you need to understand the effects of horizontal translation on the logarithmic function. The standard form of a logarithmic function is f(x) = log(base a)(x).

In this case, the function f(x) = log(base 10)x is horizontally shifted 4 units to the left. To achieve this shift, you need to subtract 4 from the variable x inside the logarithm.

Looking at the options:
a) f(x) = log(base 10)(x-4) - This is the correct option as it subtracts 4 from x inside the logarithm, resulting in a horizontal shift of 4 units to the left.
b) f(x) = 4log(base 10)X - This option multiplies the entire logarithmic function by 4, which represents a vertical stretch but does not result in a horizontal shift to the left.
c) f(x) = log(base 10) x+4 - This option adds 4 to x inside the logarithm, which would cause a horizontal shift to the right, not to the left.

Therefore, the correct answer is a) f(x) = log(base 10)(x-4).

2. To verify the answer for this question, you need to understand the effects of various transformations on the logarithmic function. The standard form of a logarithmic function is f(x) = log(base a)(x).

In this case, you are given the original function f(x) = -8log(base 10)x+6 and you need to transform it into f(x) = 4log(base 10)x+1.

Let's analyze the options:
a) reflection about the x-axis, vertical compression by a factor of 1/2, vertical translation 5 units down - The original function is reflected about the x-axis. Then, it is vertically compressed by a factor of 1/2, which entails multiplying it by 1/2. Finally, it is vertically translated 5 units down, which entails subtracting 5 from the logarithmic function. This transformation matches the desired result.
b) reflection about the y-axis, vertical stretch by a factor of 2, vertical translation 5 units up - This transformation does not match the desired result as it reflects the function about the y-axis instead of the x-axis.
c) vertical translation 5 units down, vertical compression by a factor of 1/2, reflection about the x-axis - This transformation does not match the desired result as it reflects the function about the x-axis before performing the vertical translation.
d) Reflection about the x-axis, vertical translation 5 units down, vertical compression by a factor of 1/2 - This transformation is missing the final step of reflecting the function about the x-axis.

Therefore, the correct answer is option a) reflection about the x-axis, vertical compression by a factor of 1/2, vertical translation 5 units down.

Continue answering questions 3-8 in the same format.