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mathematics
basic technical mathematics

Questions and Answers of Basic Technical Mathematics

The acceleration g (in m/s2) produced by the gravitational force of Earth on a spacecraft is given by g = 3.99 ×1014 /r2, where r is the distance from the center of Earth to the spacecraft. On
Find the logarithms of the given numbers. About 1.3 × 10−14% of carbon atoms are carbon-14, the radioactive isotope used in determining the age of samples from ancient sites.
Use a calculator to display the indicated graphs.The graph of y = log5 x
Solve for y in terms of x.log6 y = log6 4 − log6 x
Find the base b of the function y = bx if its graph passes through the point (3, 64).
Determine the value of the unknown.log10 0.01 = x
Solve the given equation.log(2x − 1) + log(x + 4) = 1
Determine the exact value of each of the given expressions.log3 (2/162)
Find the logarithms of the given numbers.The diameter of the planet Jupiter is 1.43 × 108 m.
Find the natural antilogarithms of the given logarithms.−8.04 × 10−3
Express each as a sum, difference, or multiple of logarithms. Wherever possible, evaluate logarithms of the result.log3 (92 × 63)
Display the graphs of the given functions on a calculator.(a) y = 0.1x (b) y = 0.5x (c) y = 0.9x
Determine the value of the unknown.log5 125 = x
Solve the given equation.2 logx 2 + log2 x = 3
Express each as the logarithm of a single quantity. See Example 3.1/2logb a − 2 logb 5 − 3 logb xData from Example 3We may also express a sum or difference of logarithms as the logarithm of a
Determine the exact value of each of the given expressions.log2 (1/32)
Strontium-90 decays according to the equation N = N0e−0.028t where N is the amount present after t years and N0 is the original amount. Plot N as a function of t on semilog paper if N0 = 1000
Solve the given equation. log(x + 2) + log 5 = 1
Find the logarithms of the given numbers. The signal used by some cell phones has a frequency of 9.00 × 108 Hz.
Express each as a sum, difference, or multiple of logarithms. Wherever possible, evaluate logarithms of the result. log6 5 36.
Find the natural antilogarithms of the given logarithms.−23.504
Express each as a sum, difference, or multiple of logarithms. Wherever possible, evaluate logarithms of the result.log10(1000x4)
Express each as the logarithm of a single quantity. See Example 3.2 loge 2 + 3 logeπ − loge 3Data from Example 3We may also express a sum or difference of logarithms as the logarithm of a single
Determine the value of the unknown.log4 16 = x
Express the given equations in exponential form.log1/3 3 = −1
By pumping, the air pressure in a tank is reduced by 18% each second. Thus, the pressure p (in kPa) in the tank is given by p = 101(0.82)t , where t is the time (in s). Plot the graph of p as a
Simplify the given expression.10log 3t
Find the natural antilogarithms of the given logarithms.−2.94218
Display the graphs of the given functions on a calculator.y = 0.5e−x
Solve the given equation.log2 x + log2 (x + 2) = 3
Express each as a sum, difference, or multiple of logarithms. Wherever possible, evaluate logarithms of the result. 3(²-) log3
Express the given equations in exponential form.log0.5 16 = −4
On the moon, the distance s (in ft) a rock will fall due to gravity is s = 2.66t 2 , where t is the time (in s) of fall. Plot the graph of s as a function of t for 0 ≤ t ≤ 10 s on (a) A
Simplify the given expression.log 102x
Express each as the logarithm of a single quantity. See Example 3.log4 33 + log4 9Data from Example 3We may also express a sum or difference of logarithms as the logarithm of a single
Find the natural antilogarithms of the given logarithms.−0.7429
Display the graphs of the given function on a calculator.i = 1.2(2 + 6−t)
Solve the given equation.3 ln 2 + ln(x − 1) = ln 24
Express the given equation in exponential form.log7 (1/49) = −2
Determine the type of graph paper on which the graph of the given function is a straight line. Using the appropriate paper, sketch the graph.y(2x) = 3
Use a calculator to verify the given values.log 500 − log 20 = log 25
Find the natural antilogarithms of the given logarithms.0.632
Express each as a sum, difference, or multiple of logarithms. Wherever possible, evaluate logarithms of the result.log 4√32y
Display the graphs of the given functions on a calculator.y = 0.4(0.95)3x
Solve the given equation.ln x − ln(1/3) = 1
Solve the given equation.log12x2 − log3x = 3
Find the natural logarithms of the given numbers.0.8926
Determine the type of graph paper on which the graph of the given function is a straight line. Using the appropriate paper, sketch the graph.y = 3−x
Solve the given equation.3 log2 (x − 1) = 12
Express each as the logarithm of a single quantity. See Example 3.logb √x + logb x2Data from Example 3We may also express a sum or difference of logarithms as the logarithm of a single
Express the given equations in exponential form.log10 0.01 = −2
Express each as the logarithm of a single quantity. See Example 3.−log8 R + log8 VData from Example 3We may also express a sum or difference of logarithms as the logarithm of a single
Determine the type of graph paper on which the graph of the given function is a straight line. Using the appropriate paper, sketch the graph.x√y = 4
Use a calculator to verify the given values.log 14 + log 0.5 = log 7
Find the natural antilogarithms of the given logarithms.0.0084210
Express each as a sum, difference, or multiple of logarithms. Wherever possible, evaluate logarithms of the result.log4 √48
Display the graphs of the given functions on a calculator.y = 0.1(0.252x)
Solve the given equation.9 log(2x − 1) = 3
Express the given equations in exponential form.log32 (1/8) = -0.6
Determine the type of graph paper on which the graph of the given function is a straight line. Using the appropriate paper, sketch the graph.xy3 = 10
Express as a logarithm of a single quantity.3log 2 − log y
Find the natural antilogarithms of the given logarithm.5.420
Express each as a sum, difference, or multiple of logarithms. Wherever possible, evaluate logarithms of the result.log7 196
Display the graphs of the given functions on a calculator.y = −1.5(4.15)x
Solve the given equation.2 log(3 − x) = 1
Express each as the logarithm of a single quantity. See Example 3.log5 9 − log5 3Data from Example 3We may also express a sum or difference of logarithms as the logarithm of a single
Express the given equations in exponential form.5 log243 3 = 1
Express each as the logarithm of a single quantity. See Example 3.log2 3 + log2 xData from Example 3We may also express a sum or difference of logarithms as the logarithm of a single
Express as a logarithm of a single quantity.2 log x + log 4
Find the natural antilogarithms of the given logarithm.2.190
Express each as a sum, difference, or multiple of logarithms. Wherever possible, evaluate logarithms of the result.log2 56
Display the graphs of the given functions on a calculator.y = 0.3(2.55)x
Use logarithms to evaluate the given expression. 895 73.486
Solve the given equation.2 log2 3 − log2 x = log2 45
Express the given equations in exponential form.3 log8 16 = 4
Determine the type of graph paper on which the graph of the given function is a straight line. Using the appropriate paper, sketch the graph.y = 5(10−x)
Find the natural logarithms of the given number.√0.000060808
Express each as the logarithm of a single quantity. See Example 3.logb a + logb cData from Example 3We may also express a sum or difference of logarithms as the logarithm of a single
Express each as a sum, difference, or multiple of logarithms. Wherever possible, evaluate logarithms of the result.log6 √5
Plot the graphs of the given function.y = 2ex
Solve the given equation.log2 x + log2 7 = log2 21
Express the given equations in exponential form.log 25 5 = 1/2
Determine the type of graph paper on which the graph of the given function is a straight line. Using the appropriate paper, sketch the graph.y = 3x6
Use logarithms to evaluate the given expressions.185100
Find the natural logarithms of the given numbers.(0.012937)4
Plot the graphs of the given function.y = 0.5πx
Express each as a sum, difference, or multiple of logarithms. Wherever possible, evaluate logarithms of the result. logs (7)
Express each as a sum, difference, or multiple of logarithms. Wherever possible, evaluate logarithms of the result.log3 (t2)
Solve the given equation.5 log6 (7x + 1) = 10
Express the given equations in exponential form.log15 1 = 0
Determine the type of graph paper on which the graph of the given function is a straight line. Using the appropriate paper, sketch the graph.y = 0.2x3
Find the antilogarithm of each of the given logarithms by using a calculator.−10.336
Find the natural logarithms of the given number.2.086 ×10−3
Plot the graphs of the given function.y = −5(1.6−x)
Express the given equations in exponential form.log9 9 = 1
Find the antilogarithm of each of the given logarithms by using a calculator.−2.23746
Plot the graphs of the given function.y = 0.2(10−x)
Express each as a sum, difference, or multiple of logarithms. Wherever possible, evaluate logarithms of the result.log3 6x
Solve the given equation.5 log32 x = −3
Express the given equations in exponential form.log11 121 = 2

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