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# Logarithmic/asymptote

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In exercise 53-56, begin by graphing f(x) = log2 x. Then use transformations of this graph to graph the given function. What is the vertical asymptote? Use the graphs to determine each function's domain and range.

56. h(x) = 2 + log2 x

The figure show the graph of f(x) = log x. In exercises 59-64, use transformations of this graph to graph each function. Graph and give equations of the asymptotes. Use the graphs to determine each function's domain and range.

60. g(x) = log(x-2)

64. g(x) = 2 - logx

The figure shows the graph of f(x) = ln x. In exercises 65-74, use transformations of this graph to graph each function. Graph and give equations of the asymptotes. Use the graphs to determine each function's domain and range.

68. h(x) = ln(1/2x)

72. h(x) = ln(-x)

In exercises 75-80, find the domain of each logarithmic function.

76. f(x) = log5(x+6)

80. f(x) = ln(x-7)^2

In exercises 81-100, evaluate or simplify each expression without using a calculator.

84. log 10^8

88. ln e

92. ln 1/e^7

96. ln e^13x

100. 10^log3sqrt x

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#### Solution Preview

In exercise 53-56, begin by graphing f(x) = log2 x. Then use transformations of this graph to graph the given function. What is the vertical asymptote? Use the graphs to determine each function's domain and range.

56. h(x) = 2 + log2 x

Answer: The graph is attached. The vertical asymtote is x = 0. The domain is (0, oo) and the range is (-oo, oo).

The figure show the graph of f(x) = log x. In exercises 59-64, use transformations of this graph to graph ...

#### Solution Summary

This post encompasses Logarithmic/asymptote.

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