Chapter 1 | Functions and Graphs
115
64 3 =4
279. 4 x +1 −32=0 280. 3 x /14 = 1 10 281. 10 x =7.21 282. 4·2 3 x −20=0 283. 7 3 x −2 =11 For the following exercises, solve the logarithmic equation
259.
260. e x = y 261. 9 y =150 262. b 3 =45 263. 4 −3/2 =0.125
For the following exercises, sketch the graph of the logarithmic function. Determine the domain, range, and vertical asymptote.
exactly, if possible. 284. log 3 x =0 285. log 5 x =−2
264. f ( x ) =3+ln x 265. f ( x ) = ln( x −1) 266. f ( x ) = ln(− x ) 267. f ( x ) =1−ln x 268. f ( x ) = log x −1 269. f ( x ) = ln( x +1)
286. log 4 ( x +5) =0 287. log(2 x −7) =0
288. ln x +3=2 289. log 6 ( x +9)+log 6 x =2 290. log 4 ( x +2)−log 4 ( x −1) =0 291. ln x +ln( x −2) = ln4
For the following exercises, use properties of logarithms to write the expressions as a sum, difference, and/or product
of logarithms. 270. log x 4 y
For the following exercises, use the change-of-base formula and either base 10 or base e to evaluate the given expressions. Answer in exact form and in approximate form, rounding to four decimal places.
9 a 3 b
271. log 3
292. log 5 47 293. log 7 82 294. log 6 103 295. log 0.5 211 296. log 2 π 297. log 0.2 0.452
272. ln a b 3 273. log 5 125 xy 3
xy 3 64
274. log 4
⎛ ⎝ ⎜ 6
⎞ ⎠ ⎟
275. ln
e 3
For the following exercises, solve the exponential equation exactly. 276. 5 x =125 277. e 3 x −15=0 278. 8 x =4
298. Rewrite the following expressions in terms of exponentials and simplify. a. 2cosh(ln x ) b. cosh4 x +sinh4 x c. cosh2 x −sinh2 x d. ln(cosh x +sinh x )+ln(cosh x −sinh x )
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