Chapter Test
Chapter
Chapter 8
Section
Chapter Test
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Solutions 11 Videos

Write the equation of the inverse of each function in both exponential and logarithmic form.

\displaystyle \begin{array}{llllllll} &(a) \phantom{.} y = 4^x &(b) \phantom{.} y = \log_6x \end{array}

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Q1

State the transformations that must be applied to f(x) = \log x to graph g(x).

\displaystyle g(x) = \log[2(x -4)] + 3

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Q2a

State the transformations that must be applied to f(x) = \log x to graph g(x).

\displaystyle g(x) = - \frac{1}{2}\log(x +5) -1

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Q2b

Evaluate.

\displaystyle \begin{array}{llllllll} &(a) \phantom{.} \log_3 \frac{1}{9} &(b) \phantom{.} \log_{5}100 - \log_54 \end{array}

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Q3

Evaluate.

\displaystyle \begin{array}{llllllll} &(a) \phantom{.} \log 15 + \log 40 - \log 6 \\ &(b) \phantom{.} \log_7343 = 2\log_749 \end{array}

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Q4

Express \log_4x^2 + 3\log_4y\frac{1}{3} - \log_4x as a single logarithm. Assume that x and y represent positive numbers.

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Q5

Solve 5^{x + 2} = 6^{x + 1}. Round your answer to three decimal places.

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Q6

Solve.

\displaystyle \log_4(x + 2) + \log_4( x-1) = 1

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Q7a

Solve.

\displaystyle \log_3(8x - 2 + \log_3(x - 1)) =2

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Q7b

Carbon-14 is used by scientists to estimate how long ago a plant or animal lived. The half-life of carbon-14 is 5730 years. A particular plant contained 100 g of carbon-14 at the time that it died.

a) How much carbon-14 would remain after 5730 years?

b) Write an equation to represent the amount of carbon-14 that remains after t years.

c) After how many years would 80 g of carbon -14 remain?

d) Estimate the instantaneous rate of change at 10 years.

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Q8

The equation that models the amount of time, t, in minutes that a cup of hot chocolate has been cooling as a function of its temperature, T, in degrees Celsius is t = \log(\frac{T - 22}{75}) \div \lgo(0.75). Calculate the following.

a) the cooling time if the temperature is 35^oC

b) the initial temperature of the drink.

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Q9