MAT 117 .edu
MAT 117 Practice 8
1) Write log 5M = x – 3 in exponential form. 2) Write 5t= V in logarithmic form.
3) Evaluate the following (Find EXACT ANSWERS, not calculator approximations.)
a) [pic] b) [pic] c) [pic] d) [pic] e) [pic] f) [pic] g) [pic]
h) [pic] i) [pic] j) [pic] k) [pic]
4) Given f(x) = [pic], Find the domain (interval notation)
5) Solve for x. [pic] 6) Solve for x. [pic] 7) Solve for x. [pic]
Write each of the following in terms of logarithms of x, y, and z, with no product, quotient, or exponent inside any logarithm.
8) [pic] 9) [pic]
Write the following as a single logarithm.
10) [pic] 11) [pic]
12) Use your calculator to estimate the following to 3 decimal places.
a) [pic] b) [pic] c) [pic] d) [pic]
13) What would you type into your calculator (exactly as it would show on the screen ) to graph the function f(x) = [pic]?
14) Solve for x. Find the exact values.
a) e3x = 100 b) 43x = 32x+2 c) 43x – 23 = 211 d) 5x+3 = 42x + 3
15) Find the exact value of all solutions to the equation e2x – 3ex – 40 = 0.
(No decimals or calculator approximations.)
16) Find the exact values of all solutions to the following equations.
a) lnx = 4 b) log(3x – 5) + log(x +5) = 2 c) [pic]
d) [pic] e) [pic]
(hint for d – use the change of base formula on log4x to switch to base 2)
17) Use your graphing calculator to find all solutions to the equation x2 – 6x + 9 = 4e– x
Round to 4 decimal places. (Write “No Solution” if there are no solutions)
Solutions to Practice 8 (revision 0)
1) 5x – 3 = M 2) log5V = t 3a) 4 b) [pic] c) -2 d) -3 e) [pic] f) 6 g) 45 h) [pic] i) [pic] j) [pic]
k) undefined 4) [pic] 5) [pic] 6) 5 7) -6, 5 8) 3logx + 2logw – 5logy – logz
9) [pic] 10) [pic] 11) [pic] 12a) 2.602 b) 4.025
c) 2.209 d) .737 13) ln(x2 – 7) / ln(5) (or log(x2 – 7) / log(5) ) 14a) 1.535 b) 10
c) 1.312 d) [pic] or [pic] 15) ln8 16a) e4 b) 5 c) 6 d) 4 e) -1
17) -1.7153, 2.3966, 3.3707
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