C7L4 Notes
Solving Logarithmic and HXDonential Equations
Solve. Write your answer in simplest form using integers, fractions, and
common logarithms. Then give the approximated answer rounded to the
neares thousandth.
LOG brT = x
Exf rrr:+,r,3S<` _i. v ~: ueAI
x -- # 4c-Cft?:i:FT:I # ~- urEL
LO(G Ll
frppkouJ!rif,#REtac;ac
x rxal I , JOTS:gp sea___Iriff ::ii;i#u~xp x rftjJul I , 5' grr
3 - 8x + 2
= x+ fr
4. 9x-5-7
--
.`-` --`'
--
x-c=
...
I:---.:-:,-==-`-
x= -3+ #
xpr--/,,ticFftti
5. 93X + 2 = 12
'
x-5,J=
X = 5_ +
iLfff:a!:`i
y:=so £ :I:`-ir\{;rca
6. 8 = 1 + 65x
---`,I:-::--:-:--:--J-
Ucf 3q )0 ~- 3 X„
£x = #:£Oq
i-, '£¥ -i#
c7| r` - 3 uofp L'1
x = Tc#
x--c,.3ttp
/
uff3&T = i:
HERE E=` EEu
ttif e its
X= ug#ar:Pst ie
x--0,217
7. 54X-2 = 6
8. 2 = 72x+2
-4xf3=tt#
;ia gt = :i,if .::L
( y.L|\
uoGr-i;+--,a::^prf.
#;+-d = RE
L/y--,a+
ax =, -a + iJff,$7
y--%+#
x--Jg+#
x=±+#rf.
x---I+#
x--0.b*#Le
y:*, ~ o r.rdiff -al
fs2 £``
I/iff3 gr
10. 29 = 24x+4
9. 35 = 63x-2
i-.;,.-
LjK+tl
Lf f i3 3 3.xp = :f\f tr ;
`1..--
;,prfjqp
£y=9`
:-i:-:J:-_,
•3x-,£iRE
~
oG`a:::
H¥+q =
Lf,rf ck
L LOG *3f+
4x=-U+U#.
+H#
x--`+#
x--%+RE
xts I,?a-`g
ojalq
11. ex-7
f f i\.prfF =
x--ff+-7
Xrx I,'qrfb
12. 9 = e2x
i,,'''`
--
:
?
---
in
•,18
i;,,x.
£#'
13.
8=e2x+3
:-....i
`i---=
IA.& -- f f i\ g
.--.-`
---?
#x+3
3:I:=,
14. e4X + 3 = 4
.
fueuY = rfu I
I-
4x--thl
-i=:-:-`-EE
ok-i+nI
•/, -i -.`=:..-
_
X---O
XF± -0,ybo
16. e3X-3 =45
15. 8 = e3X + 3
-L3
~3
_i -ar di,#
f ue3ff fag --f f it#*
•£x-3 --f f i.g#g
£;,,*:~
¢frl S =
_jK=3+^#S~
ffi± .£-
',;--ed¥ of ty
M5 = 3y:
/+
3 x i A sx = fu¥
3
17. 711 = e4x-2
xfursa,£&q
4 * ed. a-
18. 826 = e3X + 1
hi 7 I ( = f i gre
tin (( = I K-3`
q K-2 -- I f pJ 11
--aft
th8a{=
i ft\89S:
3*
q K = &+ fife. Fj 1{ i
+fty-7 i (
a.ELf+ffi#
X
x -- a I , 4 3 `
y\fure£,,falav
rfuL!L3-
#
19. 4e5X + 7 = 18
20. 9e3X+5 = 7
-7
-7
|Ln11~\1-I--`lrl.
L`g
:r'..
e3X+5_ rl
-
`-.-`--;
in
fu3ti=__=ffi#f
7
£¥ = -5 ,+-I
^rl a ,_±
-:-_5+thL,2S
iiiEiii
S_
xrx o,£02\
I-``,,./-
-I+ff*
i
x-rs/I,ggr3
21. In (5x) = 9
fro(3¥:-
3x='/ =
5,xr
•:.JY --
1
x-- 7¥
3 on,
y',a / 6#fJ , til r7
Xrx4r/cjt
23. 6 + ]n (2x - 1) =£
-G
th(2¥-() -a
24. 7 + 3 In (5x - 1) = 19
-7
a `f f i\, Ir;#+\) ---
'' :.1``
fy'(i") = L/
pw:w[3*-!ly -- e,L
EH=H
cfuliK-(\
a x-( = a,
`- -. `
2x= I +
5,X-)
-x'=lf_etl
5x= ) i
5L,
xf= 4' (q5~
x RE. i I , ip 3` fa
Solve.
25. log r - 1
L0C9,® r -= I
26. logs y - 3
6-3= i
= /,,i,5#
/ o' = r`
r -- / 0
27. 2 log2 w = 10
Lot?nalul -- 5,
28. Iog6 v - 5 = -3
uf if iGV -~ .-L->
£> = LU
u --- 3 2`-- `
29. Iogi3 v + 2 = 2
Life/3V = ro
4£ = V/
v -= 36-
30. Iog8 (13t - 5) = 1
8` = 13t- 5f
+i
/jo= v
\v.--:
-/
+ >_
/3 = / 3tJ
EEl
31. 1ogi2 (2t -6) = 2
/ 3a = 2L-le
/Of tl = z¢6-a
/ 50 = ,2 t
t= r7f
33.Iog64(4Z-2)=:
32. log (7r + 9) = 2
Life,,o[Tr+'#3=*ir
/ oa __ r7 r + C3
/ 00 =fr r| r + =|
9 ` i r7r
r =-13
34. Iogi6 (2z - 6) = 2
G1+ = tt%-fck
/ b%
-, ,#% - L ed
#= 42-A
t2of
= az ct,vt2
i_ --:
i-fDofjal%
J` =
i?= `'
35. log8 (-t, + 3 - 3
£oGS(-i) = a
ys#j:ffrf
36. -2 logg (-y) = 11
LOG7fl)=
`Z
83 = -€
q=-±
i= = - i
t--rf
i.-, = --j`:
i
38. 7 log y - 7
37. log t + 1 - 4
-/-(
40?oJ = l
L{J£,,Bt = 3
/ ,,f = f3
t= /000
39. logo v - logo 2 = 1
40. 1084 t - log4 1 = 4
LJD6q I -4
EEEIE,
v -ii, ltr
t = ftf g&
41. logo W + logo 9 = 1
LfoF3q qul =
q I -= tw
c^J = /
I
42. Iog8 S + log8 2 = 2
Uf i f3gf#r£ I f lf ro
83 = 2s
t a -= 3 s
5 -- 3 EL
43. Iog8 3y = log8 (5y - 8)
7J i 5-J - %`
44. Iog2 (r2 - r) = Iog2 6
r2-r = L9
--£3 =- -. a
r2-r -G = 0
(r_rf3`tr-+;``'j=o
r-3--(,J
,r+£=`„
fret(
V-
-=, r?3 i -C*
46. Iog7(w2+5w+10) = log7 (5w + 19)
45. Iog8 u2 = log8 4
H EIII
)J
Lu Z+ 5-uo + / 0 _- 5-uo + ( ci
u = +I ¢a`
h)F±rd:fS a r€3
trj* £i=~{u
ind~3 -:A {5
L)= -3, 3
47. Iog2 (y2 -6y + 15) = Iog2 (|y + 9) 48. log (-3y + 3) = log (-2y + 10)
I:-4!+`3-=-i+q±
±2- 5-j +- fe = 0
(!-j,(9 -3) =0
b~a=O
tr3=cj
tj = a-, 5
-5J+3 =-£J+,a
-j=7
`_-.:'---,..'.-.