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The Topic For Today Is…
Exponential and Logarithmic Equations
Exponential
Functions
Logarithmic
Functions
Expanding
Expressions
Condensing
Expressions
Solving
Equations
200
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400
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400
600
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800
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Exponential
Functions: 200
• Question:
Evaluate f(x) = 25-3x at x=2/3.
• Answer
0.0016 or 1/625
Exponential
Functions: 400
• Question:
What is the asymptote of f(x) = 0.3x+1?
• Answer
y=0
Exponential
Functions: 600
• Question:
Is the function increasing or decreasing?
g(x) = 0.3-x
• Answer
Decreasing
Daily Double
The Winner Of The Last Round
Write Down How Much Money
You Are Willing To Risk
If You get the Question write you win that money
If you get it wrong you Loss the money!
Exponential
Functions: 800
• Question:
A car is bought for $24,000. It depreciates at a
rate of 14.5% per year. What will the value of
the car be in 10 years?
• Answer
$5010.40
Exponential
Functions: 1000
• Question:
There are 3 options for investing $500. The
first earns 7.5% compounded annually, the
second earns 7.25% compounded quarterly,
and the second earns 7% compounded
continuously. Determine which investment
yields the highest return in 20 years.
• Answer
Option Number 1.
Logarithmic
Functions: 200
• Question:
Write as a exponential equation. log381 = 4.
• Answer
34 = 81
Logarithmic
Functions: 400
• Question:
Solve the equation for x. log662 = x
• Answer
x=2
Logarithmic
Functions: 600
• Question:
Describe the relationship between the graphs
of f and g.
f(x) = 5x
g(x) = log5x
• Answer
The graphs are symmetric around the line y =
x because f(x) and g(x) are inverse functions.
Logarithmic
Functions: 800
• Question:
Find the domain, range, vertical asymptote, and
x- and y-intercepts of f(x) = 4 log5(x + 2) - 3
• Answer
–
–
–
–
–
Domain: (0, ∞)
Range: (- ∞, ∞)
Vertical Asymptote: x = -2
x – intercept: ( 53/4 - 2, 0)
y – intercept: (0, 4 log52 – 3)
Logarithmic
Functions: 1000
• Question:
Graph f(x) = –log2(x - 4) + 5
• Answer
See the teacher for the answer.
Expanding
Expressions: 200
• Question: Expand the log.
ln (z(z + 1)2)
• Answer
ln z + 2ln(z + 1)
Expanding
Expressions: 400
• Question: Expand the natural log.
ln 3 x
y
• Answer
1
1
ln x  ln y
3
3
Expanding
Expressions: 600
• Question: Expand the natural log.
x2 1
ln( 3 )
x
• Answer
ln (x + 1) + ln (x – 1) – 3 ln x
Expanding
Expressions: 800
• Question: Expand the natural log.
4
x y
ln 5
z
• Answer
4 ln x + ln y – 5 ln z
Expanding
Expressions: 1000
• Question: Expand the log.
2
x
logb 2 3
y z
• Answer
2logb x  2logb y  3logb z
Condensing
Expressions: 200
• Question:
Condense the logarithm to a single quantity.
4[lnz + ln(z + 5)] – 2ln(z – 5)
• Answer
z 4 ( z  5)4
ln
( z  5)2
Daily Double
The Winner Of The Last Round
Write Down How Much Money
You Are Willing To Risk
If You get the Question write you win that money
If you get it wrong you Loss the money!
Condensing
Expressions: 400
• Question:
Condense the logarithm to a single quantity.
1
[2 ln( x  3)  ln x  ln( x 2  1)
3
• Answer
3
x( x  3) 2
x2 1
Condensing
Expressions: 600
• Question:
Condense the logarithm to a single quantity.
2[ln x – ln(x + 1) – ln(x – 1)]
• Answer
x2
ln 2
( x  1)2
Condensing
Expressions: 800
• Question:
Condense the logarithm to a single quantity.
1
[ln y  2 ln( y  4)]  ln( y  1)
3
• Answer
3
ln
y( y  4)2
y 1
Condensing
Expressions:
1000
• Question:
Condense the logarithm to a single quantity.
1
[ln( x  1)  2 ln( x  1)]  3ln x
2
• Answer:
ln( x ( x  1) x  1)
3
Solving
Equations: 200
• Question:
Solve ln(2x – 1) = 5. Round to the nearest
hundredth.
• Answer
e 1
 74.71
2
5
Solving
Equations: 400
• Question:
Solve e2x – 4ex – 5 = 0. Round to 3 decimal
places.
• Answer
ln5≈1.609
Solving
Equations: 600
• Question:
Solve -2 + 2ln(3x) = 17. Round to 3 decimal
places.
• Answer
4453.242
Solving
Equations: 800
• Question:
Solve ln(x + 5) = ln(x – 1) – ln (x + 1)
• Answer
No real solution.
Solving
Equations: 1000
• Question: Solve and round to 3 decimal
places.
log 8 x  log(1  x )  2
• Answer
180.384