 5.1: fx ln x 3
 5.2: fx lnx 3
 5.3: In Exercises 3 and 4, use the properties of logarithms to expand th...
 5.4: In Exercises 3 and 4, use the properties of logarithms to expand th...
 5.5: In Exercises 5 and 6, write the expression as the logarithm of a si...
 5.6: In Exercises 5 and 6, write the expression as the logarithm of a si...
 5.7: In Exercises 7 and 8, solve the equation for x.ln x 1 2
 5.8: In Exercises 7 and 8, solve the equation for x.ln x lnx 3 0
 5.9: In Exercises 914, find the derivative of the function.gx ln2x
 5.10: In Exercises 914, find the derivative of the function.hx ln xx 1 x 2
 5.11: In Exercises 914, find the derivative of the function.fx xln x
 5.12: In Exercises 914, find the derivative of the function.fx lnxx2 22 3
 5.13: In Exercises 914, find the derivative of the function.y 1 b2 a bx a...
 5.14: In Exercises 914, find the derivative of the function.y 1 ax b a2 l...
 5.15: In Exercises 15 and 16, find an equation of the tangent line to the...
 5.16: In Exercises 15 and 16, find an equation of the tangent line to the...
 5.17: In Exercises 1724, find or evaluate the integral.1 7x 2 dx
 5.18: In Exercises 1724, find or evaluate the integral.x x2 1 dx
 5.19: In Exercises 1724, find or evaluate the integral.sin x 1 cos x dx
 5.20: In Exercises 1724, find or evaluate the integral.ln x x dx
 5.21: In Exercises 1724, find or evaluate the integral.4 1 2x 1 2x dx
 5.22: In Exercises 1724, find or evaluate the integral.e 1 ln x x dx
 5.23: In Exercises 1724, find or evaluate the integral.3 0 sec d
 5.24: In Exercises 1724, find or evaluate the integral.4 0 tan 4 x dx
 5.25: In Exercises 2530, (a) find the inverse function of (b) use a graph...
 5.26: In Exercises 2530, (a) find the inverse function of (b) use a graph...
 5.27: In Exercises 2530, (a) find the inverse function of (b) use a graph...
 5.28: In Exercises 2530, (a) find the inverse function of (b) use a graph...
 5.29: In Exercises 2530, (a) find the inverse function of (b) use a graph...
 5.30: In Exercises 2530, (a) find the inverse function of (b) use a graph...
 5.31: In Exercises 3134, verify that has an inverse. Then use the functio...
 5.32: In Exercises 3134, verify that has an inverse. Then use the functio...
 5.33: In Exercises 3134, verify that has an inverse. Then use the functio...
 5.34: In Exercises 3134, verify that has an inverse. Then use the functio...
 5.35: In Exercises 35 and 36, (a) find the inverse function of (b) use a ...
 5.36: In Exercises 35 and 36, (a) find the inverse function of (b) use a ...
 5.37: In Exercises 37 and 38, graph the function without the aid of a gra...
 5.38: In Exercises 37 and 38, graph the function without the aid of a gra...
 5.39: In Exercises 39 44, find the derivative of the function.gt t2 et
 5.40: In Exercises 39 44, find the derivative of the function.gx ln ex 1 ex
 5.41: In Exercises 39 44, find the derivative of the function.y e2x e2x
 5.42: In Exercises 39 44, find the derivative of the function.hz ez2 2
 5.43: In Exercises 39 44, find the derivative of the function.\gx x2 e
 5.44: In Exercises 39 44, find the derivative of the function.y 3e3 t
 5.45: In Exercises 45 and 46, find an equation of the tangent line to the...
 5.46: In Exercises 45 and 46, find an equation of the tangent line to the...
 5.47: y ln x y 2 0
 5.48: cos x2 xey
 5.49: In Exercises 4956, find or evaluate the integral
 5.50: In Exercises 4956, find or evaluate the integral
 5.51: In Exercises 4956, find or evaluate the integral
 5.52: In Exercises 4956, find or evaluate the integral
 5.53: In Exercises 4956, find or evaluate the integral
 5.54: In Exercises 4956, find or evaluate the integral
 5.55: In Exercises 4956, find or evaluate the integral
 5.56: In Exercises 4956, find or evaluate the integral
 5.57: Show that satisfies the differential equation y 2y 10y 0.
 5.58: The value of an item years after it is purchased is (a) Use a graph...
 5.59: In Exercises 59 and 60, find the area of the region bounded by the ...
 5.60: In Exercises 59 and 60, find the area of the region bounded by the ...
 5.61: In Exercises 6164, sketch the graph of the function by hand
 5.62: In Exercises 6164, sketch the graph of the function by hand
 5.63: In Exercises 6164, sketch the graph of the function by hand
 5.64: In Exercises 6164, sketch the graph of the function by hand
 5.65: fx 3x1
 5.66: fx 4ex
 5.67: y x 2x1
 5.68: y x4x
 5.69: gx log3 1 x
 5.70: hx log5 x x 1
 5.71: In Exercises 71 and 72, find the indefinite integral.
 5.72: In Exercises 71 and 72, find the indefinite integral.
 5.73: The time (in minutes) for a small plane to climb to an altitude of ...
 5.74: (a) How large a deposit, at 5% interest compounded continuously, mu...
 5.75: fx 2 arctanx 3
 5.76: hx 3 arcsin 2x
 5.77: In Exercises 77 and 78, evaluate the expression without using a cal...
 5.78: In Exercises 77 and 78, evaluate the expression without using a cal...
 5.79: In Exercises 79 84, find the derivative of the function.y tanarcsin x
 5.80: In Exercises 79 84, find the derivative of the function.y arctanx y...
 5.81: In Exercises 79 84, find the derivative of the function.y x arcsec x
 5.82: In Exercises 79 84, find the derivative of the function.y 1 2 arcta...
 5.83: In Exercises 79 84, find the derivative of the function.y xarcsin x...
 5.84: In Exercises 79 84, find the derivative of the function.y x 2 < x <...
 5.85: 1 e2x e2x dx
 5.86: 1 3 25x2 dx
 5.87: x 1 x4 dx
 5.88: 1 16 x2 dx
 5.89: arctanx 2 4 x2 dx
 5.90: arcsin 2x 1 4x2 dx
 5.91: In Exercises 91 and 92, find the area of the region.
 5.92: In Exercises 91 and 92, find the area of the region.
 5.93: A weight of mass is attached to a spring and oscillates with simple...
 5.94: In Exercises 94 and 95, find the derivative of the function
 5.95: In Exercises 94 and 95, find the derivative of the function
 5.96: In Exercises 96 and 97, find the indefinite integral.
 5.97: In Exercises 96 and 97, find the indefinite integral.
Solutions for Chapter 5: Logarithmic, Exponential, and Other Transcendental Functions
Full solutions for Calculus  9th Edition
ISBN: 9780547167022
Solutions for Chapter 5: Logarithmic, Exponential, and Other Transcendental Functions
Get Full SolutionsSince 97 problems in chapter 5: Logarithmic, Exponential, and Other Transcendental Functions have been answered, more than 60945 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Calculus , edition: 9. Chapter 5: Logarithmic, Exponential, and Other Transcendental Functions includes 97 full stepbystep solutions. Calculus was written by and is associated to the ISBN: 9780547167022.

Characteristic polynomial of a square matrix A
det(xIn  A), where A is an n x n matrix

Equation
A statement of equality between two expressions.

Expanded form of a series
A series written explicitly as a sum of terms (not in summation notation).

Extraneous solution
Any solution of the resulting equation that is not a solution of the original equation.

Line of symmetry
A line over which a graph is the mirror image of itself

Multiplication principle of probability
If A and B are independent events, then P(A and B) = P(A) # P(B). If Adepends on B, then P(A and B) = P(AB) # P(B)

Multiplication property of inequality
If u < v and c > 0, then uc < vc. If u < and c < 0, then uc > vc

nth root of unity
A complex number v such that vn = 1

Opens upward or downward
A parabola y = ax 2 + bx + c opens upward if a > 0 and opens downward if a < 0.

Opposite
See Additive inverse of a real number and Additive inverse of a complex number.

Outliers
Data items more than 1.5 times the IQR below the first quartile or above the third quartile.

Quadratic function
A function that can be written in the form ƒ(x) = ax 2 + bx + c, where a, b, and c are real numbers, and a ? 0.

Random numbers
Numbers that can be used by researchers to simulate randomness in scientific studies (they are usually obtained from lengthy tables of decimal digits that have been generated by verifiably random natural phenomena).

Reflection through the origin
x, y and (x,y) are reflections of each other through the origin.

Riemann sum
A sum where the interval is divided into n subintervals of equal length and is in the ith subinterval.

Righthand limit of ƒ at x a
The limit of ƒ as x approaches a from the right.

Second
Angle measure equal to 1/60 of a minute.

Stretch of factor c
A transformation of a graph obtained by multiplying all the xcoordinates (horizontal stretch) by the constant 1/c, or all of the ycoordinates (vertical stretch) of the points by a constant c, c, > 1.

Symmetric property of equality
If a = b, then b = a

xcoordinate
The directed distance from the yaxis yzplane to a point in a plane (space), or the first number in an ordered pair (triple), pp. 12, 629.