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What is the true solution to the equation? 2 ln e raised to the natural log 2 power minus the natural log of e raised to the natural log 10 power is equal to natural log 30

A
x is equal to 300
B
x is equal to 75
C
x is equal to 150
D
x is equal to 30
2
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What is the value of e raised to the natural log 7 power ?

A
1
B
7
C
7 e
D
7 x
3

What is the range of the function y is equal to 4 e to the x th power ?

A
all real numbers less than 4
B
all real numbers greater than 0
C
all real numbers greater than 4
D
all real numbers less than 0
4

What is the value of the natural log of e to the 4th power ?

A
1
B
2
C
4
D
0
5

What is 3 ln 3 minus natural log 9 expressed as a single natural logarithm?

A
natural log 6
B
natural log 18
C
natural log 3
D
natural log 27
6

Which of the following shows the graph of y is equal to 2 e to the x th power ?

A
Image with description "Image 1: On a coordinate plane the x axis lists from negative 5 to 5 by 1 and y axis lists from negative 5 to 5 by 1. A single curve is plotted, with a horizontal asymptote at y equals 0 (the x-axis) as x approaches negative infinity. It crosses the x-axis at (negative 4 comma 0) and the y-axis at (0 comma 2) and passes through (0 point 5 comma 4). Image 2: On a coordinate plane the x axis lists from negative 5 to 5 by 1 and y axis lists from negative 5 to 5 by 1. The curve starts at the point (0 comma negative 3). It then increases as x increases, curving upwards and to the right. It intersects the x axis at (1 comma 0). The curve passes through the points (2 comma 0 point 5) and (4 comma 1 point 5). Image 3: On a coordinate plane the x axis lists from negative 5 to 5 by 1 and y axis lists from negative 5 to 5 by 1. The curve has a vertical asymptote at x equals 0, extending downwards towards negative infinity as x approaches 0 from the positive side. The curve passes through (0 point 5 comma negative 1 point 5), the x-intercept (1 comma 0), and (2 point 7 comma 2). It is an increasing function, extending upwards and to the right. Image 4: On a coordinate plane the x axis lists from negative 5 to 5 by 1 and y axis lists from negative 5 to 5 by 1. The curve has a horizontal asymptote at y equals 0 as x approaches negative infinity. It crosses the x-axis at (negative 4 comma 0) and the y-axis at (0 comma 4). It passes through points (negative 2 comma 0 point 5), (negative 1 comma 1 point 5) and ( negative 0 point 5 comma 3)."
B
Image with description "Image 1: On a coordinate plane the x axis lists from negative 5 to 5 by 1 and y axis lists from negative 5 to 5 by 1. A single curve is plotted, with a horizontal asymptote at y equals 0 (the x-axis) as x approaches negative infinity. It crosses the x-axis at (negative 4 comma 0) and the y-axis at (0 comma 2) and passes through (0 point 5 comma 4). Image 2: On a coordinate plane the x axis lists from negative 5 to 5 by 1 and y axis lists from negative 5 to 5 by 1. The curve starts at the point (0 comma negative 3). It then increases as x increases, curving upwards and to the right. It intersects the x axis at (1 comma 0). The curve passes through the points (2 comma 0 point 5) and (4 comma 1 point 5). Image 3: On a coordinate plane the x axis lists from negative 5 to 5 by 1 and y axis lists from negative 5 to 5 by 1. The curve has a vertical asymptote at x equals 0, extending downwards towards negative infinity as x approaches 0 from the positive side. The curve passes through (0 point 5 comma negative 1 point 5), the x-intercept (1 comma 0), and (2 point 7 comma 2). It is an increasing function, extending upwards and to the right. Image 4: On a coordinate plane the x axis lists from negative 5 to 5 by 1 and y axis lists from negative 5 to 5 by 1. The curve has a horizontal asymptote at y equals 0 as x approaches negative infinity. It crosses the x-axis at (negative 4 comma 0) and the y-axis at (0 comma 4). It passes through points (negative 2 comma 0 point 5), (negative 1 comma 1 point 5) and ( negative 0 point 5 comma 3)."
C
Image with description "Image 1: On a coordinate plane the x axis lists from negative 5 to 5 by 1 and y axis lists from negative 5 to 5 by 1. A single curve is plotted, with a horizontal asymptote at y equals 0 (the x-axis) as x approaches negative infinity. It crosses the x-axis at (negative 4 comma 0) and the y-axis at (0 comma 2) and passes through (0 point 5 comma 4). Image 2: On a coordinate plane the x axis lists from negative 5 to 5 by 1 and y axis lists from negative 5 to 5 by 1. The curve starts at the point (0 comma negative 3). It then increases as x increases, curving upwards and to the right. It intersects the x axis at (1 comma 0). The curve passes through the points (2 comma 0 point 5) and (4 comma 1 point 5). Image 3: On a coordinate plane the x axis lists from negative 5 to 5 by 1 and y axis lists from negative 5 to 5 by 1. The curve has a vertical asymptote at x equals 0, extending downwards towards negative infinity as x approaches 0 from the positive side. The curve passes through (0 point 5 comma negative 1 point 5), the x-intercept (1 comma 0), and (2 point 7 comma 2). It is an increasing function, extending upwards and to the right. Image 4: On a coordinate plane the x axis lists from negative 5 to 5 by 1 and y axis lists from negative 5 to 5 by 1. The curve has a horizontal asymptote at y equals 0 as x approaches negative infinity. It crosses the x-axis at (negative 4 comma 0) and the y-axis at (0 comma 4). It passes through points (negative 2 comma 0 point 5), (negative 1 comma 1 point 5) and ( negative 0 point 5 comma 3)."
D
Image with description "Image 1: On a coordinate plane the x axis lists from negative 5 to 5 by 1 and y axis lists from negative 5 to 5 by 1. A single curve is plotted, with a horizontal asymptote at y equals 0 (the x-axis) as x approaches negative infinity. It crosses the x-axis at (negative 4 comma 0) and the y-axis at (0 comma 2) and passes through (0 point 5 comma 4). Image 2: On a coordinate plane the x axis lists from negative 5 to 5 by 1 and y axis lists from negative 5 to 5 by 1. The curve starts at the point (0 comma negative 3). It then increases as x increases, curving upwards and to the right. It intersects the x axis at (1 comma 0). The curve passes through the points (2 comma 0 point 5) and (4 comma 1 point 5). Image 3: On a coordinate plane the x axis lists from negative 5 to 5 by 1 and y axis lists from negative 5 to 5 by 1. The curve has a vertical asymptote at x equals 0, extending downwards towards negative infinity as x approaches 0 from the positive side. The curve passes through (0 point 5 comma negative 1 point 5), the x-intercept (1 comma 0), and (2 point 7 comma 2). It is an increasing function, extending upwards and to the right. Image 4: On a coordinate plane the x axis lists from negative 5 to 5 by 1 and y axis lists from negative 5 to 5 by 1. The curve has a horizontal asymptote at y equals 0 as x approaches negative infinity. It crosses the x-axis at (negative 4 comma 0) and the y-axis at (0 comma 4). It passes through points (negative 2 comma 0 point 5), (negative 1 comma 1 point 5) and ( negative 0 point 5 comma 3)."
7

What is the true solution to 3 ln 2 plus natural log 8 is equal to 2 ln 4 x ?

A
x is equal to 2
B
x is equal to 1
C
x is equal to 8
D
x is equal to 4
8

Which of the following shows the graph of y is equal to 2 ln x ?

A
Image with description A coordinate plane with a horizontal x-axis and vertical y-axis both labeled from negative 5 to 5 in increments of 1. A curve extends horizontally along the negative x-axis, curves upward to pass through 0 comma 2, and rises sharply before 1 on the x-axis into the first quadrant.
B
Image with description A coordinate plane with a horizontal x-axis and vertical y-axis both labeled from negative 5 to 5 in increments of 1. A curve extends horizontally along the negative x-axis, curves upward through 0 comma 1, and rises sharply before 1 on the x-axis into the first quadrant.
C
Image with description A coordinate plane with a horizontal x-axis and vertical y-axis both labeled from negative 5 to 5 in increments of 1. A curve extends upward along the negative y-axis from near negative 5, passes through the horizontal x-axis at 1 comma 0, and rises gradually through the first quadrant passing through approximately 3 comma 2.
D
Image with description A coordinate plane with a horizontal x-axis and vertical y-axis both labeled from negative 5 to 5 in increments of 1. A curve extends upward from 0 comma negative 1 on the vertical y-axis, crosses the horizontal x-axis between the origin and 1, and rises gradually through the first quadrant passing through 4 comma 2.
9

What is the true solution to 2 ln e raised to the natural log 5 power is equal to 2 ln 15 ?

A
x is equal to 3
B
x is equal to 0
C
x is equal to 15
D
x is equal to 9
10

What is the true solution to 2 ln 4 x is equal to 2 ln 8 ?

A
x is equal to negative 4
B
x is equal to 2
C
x is equal to negative 2
D
x is equal to 4

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Base e — Quiz Answers — Precalculus