essential questions: 1. how do i solve exponential functions? 2. how do i solve logarmithic...
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Essential Questions:1. How do I solve exponential functions?2. How do I solve logarmithic functions?
Change-of-Base Formula
Let a, b, and x be positive real numbers such that a1 and b1.
a
xxa log
loglog
Evaluate using the natural logarithms. Round to four decimal places.
log3 73log
7log 1.7712
1. Isolate the base.
2. If you can rewrite to make the same base, do it!
3. If not,
a) Rewrite an Exponential Equation in log form.
b) Rewrite a Logarithmic Equation in exp. Form.
4. CHECK YOUR ANSWER!!
Ex. 1
8 23x 8log 23x
log 23
log8x
1.508x
Storing in Calc as “x” :1.508 x®take last answer
sto (button above on)
x (button above sto)
enter
®
72xe2n 7l lnxe
72lnx
277.4x
Ex. 2
Storing in Calc as “x” :4.277 x®take last answer
sto (button above on)
x (button above sto)
enter
®
42)2(3 x
14)2( x
14log2xlog14
xlog2
=
807.3x
Ex. 3
Storing in Calc as “x” :3.807 x®take last answer
sto (button above on)
x (button above sto)
enter
®
2 52(3 ) 4 11t 2 52(3 ) 15t
2 5 153
2t
3
152 5 log
2t
3
152 log 5
2 t
3
15log 5
22
t
3.417t
Ex. 4
2 53 3log l
152
og3 t
Storing in Calc as “x” :3.417 x®take last answer
sto (button above on)
x (button above sto)
enter
®
Ex. 5
.53 2 5xe
.5n l 1l nxe
.5 ln1x
0x
.5 1xe
.53 3xe
Storing in Calc as “x” : 0 x®take last answer
sto (button above on)
x (button above sto)
enter
®
Ex. 6 – Log Equations
52log (3 ) 4x
5log (3 ) 2x
23 5x3 25x
253
x
5 55log (3 ) 2x
Ex. 7 – Log Equations
log 5 5 3xlog 5 2x
25 10x5 100x20x
10 10log 5 3x
Ex. 8 – Log Equations
5 2ln 4x2ln 1x
1
ln2
x
12x e
0.607x
Ex. 9 – Log Equations
log log( 3) 1x x log ( 3) 1x x
1( 3) 10x x
2 3 10x x
2 3 10 0x x
( 5)( 2) 0x x
5, 2x x 2x
10 10log ( 3) 1 x x
Ex. 10 – Log Equations
log log( 3) 1 x x
log 13
x
x
103
x
x
10 3 x x
10 30 x x10 10log 1
3
x
x 9 30 x3.333x
NO SOLUTION
Ex. 11 – Last Exponential!!
2 4 5 0x xe e
5 1 0x xe e
5 0 1 0x xe e
5xe 1xe
ln ln5xe ln l ( 1)nxe 1.609x Not Possible
Homework
3A.4 Worksheet