### Logarithm's Review

Hi guys, this is Jess and im supposed to have my scribe post to be done by yesterday but since my **dad **took away the computer and i had work after school till like 1030 so i couldn't have it up on time. Im sorry! Anyways, on monday, all we did in class with Mr. K were to review stuffs about logarithms, word problems and corrected our very first online quiz!

Here's the first one:

1. Which of the following best defines the inverse of ƒ(x) = e^x + 3?

f(x) = e^x + 3

y = e^x + 3

x = e^y + 3

x - 3 = e^y

ln (x-3) = y

2. If $1000 is invested in an account that pays 6% per year, compounded quarterly, how much will be in the account at the end of 10 years?

A = ?

Ao = 1000

r = 0.06

n = 4 (quarterly)

t = 10

A = Ao (1 + (r/n))^nt

A = 1000 (1 + (0.06/4))^(4)(10)

A = 1000 (1.015)^40

A = 1000 (1.814018409)

A = 1814.02

3. How much should be invested in an account that pays 6% per year, compounded continuously, so that there will be $10 000.00 in the account ten years from now?

Conpounded continuously formula: A = Pe^rt

A = 10 000

P = ?

r = 0.06

t = 10

10 000 = P(e)^(0.06)(10)

10 000 = P(e)^(0.6)

10 000 = P(1.8221188)

P = 5488.11

4. Ann’s initial investment doubles in 5 years. If interest is compounded continuously, at what rate did Anna invest her money?

A = 2

P = 1

r = ?

t = 5

and A = Pe^rt

2 = 1(e)^5r

2 = e^5r

ln (2) = 5r

(1/5) ln (2) = r

5. Suppose that a > 0. The graph of f(x) (illustrated) has a horizontal asymptote. What is the equation of the horizontal asymptote?

f(x) = b + e^-ax

y = b + e^-ax

b is the vertical shift

a is the horizonal compression

"-" reflects over the x-axis

=> horizontal asymptote y = b

6. What is the domain of f(x) = ln(2-x)?

x<2, and the argument have to be positive, not negative or either zero

therefore D(-∞,2)

7. The solution of 5^2x = 7 is (1/2) log base 5 to 7

5^2x = 7

2x log 5 = log 7

2x = log 7 / log 5

x = (1/2) (log7/log5)

* base on the " change of base law "

therefore (1/2) (log7/log5) = (1/2) log base 5 to 7 x

8. Solve for x: log(2x + 3) = 5

log(2x + 3) = 5

10^5 = 2x + 3

100 000 = 2x + 3

99997 = 2x

x = 99997/2

9.Which of the following expressions is equivalent to ln a / ln b

* Base on the " change of base law "

ln a / ln b = log base of b to a

10. Which of the following choices is equivalent to: e^ln x + ln y

e^ln x + ln y

e^ln(x)(y)

xy

11. If x > 0, then find an expression equivalent to:10^-2log(1/x)

10^-2log(1/x)

10^(log(1/x)^(-2))

10^(log x ^ 2)

x^2

And here's another word problem that we had on that class day.

An archearchaeologists finds a fossil that contains 60mg of Carbon-14. She knows the bone originally contained 100mg of Carbon-14. How old is the fossil if the half life of Carbon-14 is 5700 years?

A = 100

Ao = 60

m = o.5

t = ?

p = 5700

A = Ao(m)^t/p

100 = 60 (.5)^t/5700

0.6 = (1/2)^t/5700

ln (0.6) = t/5700 ln (1/2)

5700 ln (0.6) = t ln (1/2)

(5700 ln (0.6)) / ln (1/2) = t

And this was all we did on Monday. Once again, sorry for had it up late. Hope you guys did good on the test :). And by the way, thanks Steve for being the scribe for today's class!

And if i had done anything wrong in my scribe post, please let me know so i can fix it. Thanks!

Goodnight everyone :)

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