Essential Questions: 1. How do I solve exponential functions? 2. How do I solve logarmithic...
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Transcript of 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?
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Change-of-Base Formula
Let a, b, and x be positive real numbers such that a1 and b1.
a
xxa log
loglog
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Evaluate using the natural logarithms. Round to four decimal places.
log3 73log
7log 1.7712
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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!!
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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
®
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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
®
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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
®
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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
®
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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
®
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Ex. 6 – Log Equations
52log (3 ) 4x
5log (3 ) 2x
23 5x3 25x
253
x
5 55log (3 ) 2x
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Ex. 7 – Log Equations
log 5 5 3xlog 5 2x
25 10x5 100x20x
10 10log 5 3x
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Ex. 8 – Log Equations
5 2ln 4x2ln 1x
1
ln2
x
12x e
0.607x
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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
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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
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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
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Homework
3A.4 Worksheet