C Challenge

Find the least integer greater than each number. Do not use a calculator.

80. log 3 38 log base 3 , 38
81. log 1.5 2.5 log base 1.5 . 2.5
82. log 7 50 log base square root of 7 . square root of 50
83. log 5 1 47 log base 5 . 1 forty seventh
84. Match each function with the graph of its inverse.

    y = log 3 x y equals , log base 3 , x y = log 2 4 x y equals , log base 2 . 4 to the x y = log 1 2 x y equals . log base 1 half . x

Standardized Test Prep

SAT/ACT

85. Which is the logarithmic form of the exponential equation 2 3 = 8 ? 2 cubed , equals 8 question mark
    1. log 8 2 = 3 log base 8 , 2 equals 3
    2. log 8 3 = 2 log base 8 , 3 equals 2
    3. log 3 8 = 2 log base 3 , 8 equals 2
    4. log 2 8 = 3 log base 2 , 8 equals 3
86. Dan will begin advertising his video production business online using a pay-per-click method, which charges $30 as an initial fee, plus a fixed amount each time the ad is clicked. Dan estimates that with the cost of 8 cents per click, his ad will be clicked about 150 times per day. Which expression represents Dan's total estimated cost of advertising, in dollars, after x days?
    6. ( 30 + 0 . 08 x ) 150 open 30 plus 0 . , 08 to the x , close 150
    7. 360 x 360 to the x
    8. 30 + 1200 x 30 plus , 1200 to the x
    9. 30 + 12 x 30 plus , 12 to the x
87. Which translation takes y = | x | y equals vertical line x vertical line  to y = y equals   | x + 3 | − 1 ? vertical line x plus 3 vertical line negative 1 question mark
    1. 3 units right, 1 unit down
    2. 3 units right, 1 unit up
    3. 3 units left, 1 unit down
    4. 3 units left, 1 unit up

Short Response

88. What is the expression ( a ) 7 3 cube root of open square root of eh close to the seventh end root ,  written as a variable raised to a single rational exponent?

Mixed Review

See Lesson 7-2.

Graph each function.

89. y = 5 x − 100 y equals 5 x minus 100
90. y = − 10 ( 4 ) x + 2 y equals negative 10 . open 4 close super x plus 2 end super
91. y = − 27 ( 3 ) x − 1 + 9 y equals negative 27 . open 3 close super x minus 1 end super . plus 9

See Lesson 4-4.

Factor each expression.

92. 4 x 2 − 8 x + 3 4 x squared , minus 8 x plus 3
93. 4 b 2 − 100 4 b squared , minus 100
94. 5 x 2 + 13 x − 6 5 x squared , plus 13 x minus 6

See Lesson 1-3.

Get Ready! To prepare for Lesson 7-4, do Exercises 95-98.

Evaluate each expression for the given value of the variable.

95. x 2 − x ; x = 2 x squared , minus x semicolon x equals 2
96. x 3 · x 5 ; x = 2 x cubed , middle dot , x to the fifth , semicolon x equals 2
97. x 8 x 10 ; x = 2 fraction x to the eighth , over x to the tenth end fraction . semicolon x equals 2
98. x 3 + x 2 ; x = 2 x cubed , plus , x squared , semicolon x equals 2

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