# A few math problems.

• Jan 11th 2010, 07:54 PM
Lokith
A few math problems.
I missed an entire week of school and my teacher is still requiring me to do a test tomorrow. She gave me a review packet and I could use some help on a few problems. If someone could answer it, show the steps and explain them to me I would greatly appreciate it.

Problems -

1. Given log c (3) = 1.857 and log c (2) = 1.214, evaluate

a) log c √12

b) log c 3/2

2. A new television show has just premiered. The number of people who watch the show can be modeled by the function N(t)=3(1.15) where N(t) is the number of millions of viewers and t is the time, in months, since the show was first introduced.

a) Evaluate N(4) to the nearest thousands and explain what this means in terms of show.

b) Find t, to the nearest thousandth such that N(t) = 4 and explains what this means in terms of the show.

3. Given f(x) = log 4 (x) then f(8) equals?

4. The graphs of y = log 2 (x) and 2^y = x:

(a) intersect only at one point
(b)intersect at 2 points
(c)are the same graph
(d)dont intersect at all
• Jan 11th 2010, 08:28 PM
Prove It
Quote:

Originally Posted by Lokith
I missed an entire week of school and my teacher is still requiring me to do a test tomorrow. She gave me a review packet and I could use some help on a few problems. If someone could answer it, show the steps and explain them to me I would greatly appreciate it.

Problems -

1. Given log c (3) = 1.857 and log c (2) = 1.214, evaluate

a) log c √12

b) log c 3/2

2. A new television show has just premiered. The number of people who watch the show can be modeled by the function N(t)=3(1.15) where N(t) is the number of millions of viewers and t is the time, in months, since the show was first introduced.

a) Evaluate N(4) to the nearest thousands and explain what this means in terms of show.

b) Find t, to the nearest thousandth such that N(t) = 4 and explains what this means in terms of the show.

3. Given f(x) = log 4 (x) then f(8) equals?

4. The graphs of y = log 2 (x) and 2^y = x:

(a) intersect only at one point
(b)intersect at 2 points
(c)are the same graph
(d)dont intersect at all

1. a) $\log_c{\sqrt{12}} = \log_c{12^{\frac{1}{2}}}$

$= \frac{1}{2}\log_c{12}$

$= \frac{1}{2}\log_c{(2\cdot 2\cdot 3)}$

$= \frac{1}{2}(2\log_c{2} + \log_c{3})$

$= \log_c{2} + \frac{1}{2}\log_c{3}$.

b) $\log_c{\frac{3}{2}} = \log_c{3} - \log_c{2}$.
• Jan 11th 2010, 08:32 PM
Prove It
Quote:

Originally Posted by Lokith
I missed an entire week of school and my teacher is still requiring me to do a test tomorrow. She gave me a review packet and I could use some help on a few problems. If someone could answer it, show the steps and explain them to me I would greatly appreciate it.

Problems -

1. Given log c (3) = 1.857 and log c (2) = 1.214, evaluate

a) log c √12

b) log c 3/2

2. A new television show has just premiered. The number of people who watch the show can be modeled by the function N(t)=3(1.15) where N(t) is the number of millions of viewers and t is the time, in months, since the show was first introduced.

a) Evaluate N(4) to the nearest thousands and explain what this means in terms of show.

b) Find t, to the nearest thousandth such that N(t) = 4 and explains what this means in terms of the show.

3. Given f(x) = log 4 (x) then f(8) equals?

4. The graphs of y = log 2 (x) and 2^y = x:

(a) intersect only at one point
(b)intersect at 2 points
(c)are the same graph
(d)dont intersect at all

$f(x) = \log_4{x}$

$f(8) = \log_4{8}$

$= \log_4{(4 \cdot 2)}$

$= \log_4{4} + \log_4{2}$

$= 1 + \log_4{4^{\frac{1}{2}}}$

$= 1 + \frac{1}{2}\log_4{4}$

$= 1 + \frac{1}{2}\cdot 1$

$= 1 + \frac{1}{2}$

$= \frac{3}{2}$.
• Jan 11th 2010, 08:32 PM
Amer
Quote:

Originally Posted by Lokith
I missed an entire week of school and my teacher is still requiring me to do a test tomorrow. She gave me a review packet and I could use some help on a few problems. If someone could answer it, show the steps and explain them to me I would greatly appreciate it.

Problems -

1. Given log c (3) = 1.857 and log c (2) = 1.214, evaluate

a) log c √12

b) log c 3/2

you should know

$1)\;\; \log a + \log b = \log ab$

$2)\;\; \log a - \log b = \log \frac{a}{b}$

$3)\;\; a \cdot \log x = \log x^a$

so
you have $\log c(2) =1.857 \;\; and\;\; \log c (3) = 1.214$

$\log c \sqrt{12} = \log c \sqrt{4\cdot 3} = \log c \cdot 2\sqrt{3}$

use the first one

$\log c(2)\cdot \sqrt{3} = \log c(2) + \log \sqrt{3} = 1.857 + \frac{\log 3}{2}$

find log 3 use the calculator

$\log \left(c \cdot \frac{3}{2}\right) = \log \left(\frac{c(3)}{2}\right) = \log c(3) - \log 2$

you have log c(3) and find log 2 using calculator
• Jan 11th 2010, 08:32 PM
Prove It
Quote:

Originally Posted by Lokith
I missed an entire week of school and my teacher is still requiring me to do a test tomorrow. She gave me a review packet and I could use some help on a few problems. If someone could answer it, show the steps and explain them to me I would greatly appreciate it.

Problems -

1. Given log c (3) = 1.857 and log c (2) = 1.214, evaluate

a) log c √12

b) log c 3/2

2. A new television show has just premiered. The number of people who watch the show can be modeled by the function N(t)=3(1.15) where N(t) is the number of millions of viewers and t is the time, in months, since the show was first introduced.

a) Evaluate N(4) to the nearest thousands and explain what this means in terms of show.

b) Find t, to the nearest thousandth such that N(t) = 4 and explains what this means in terms of the show.

3. Given f(x) = log 4 (x) then f(8) equals?

4. The graphs of y = log 2 (x) and 2^y = x:

(a) intersect only at one point
(b)intersect at 2 points
(c)are the same graph
(d)dont intersect at all

4. Hint: If $y = \log_a{x}$ then $x = a^y$...
• Jan 11th 2010, 08:50 PM
Lokith
Thanks for the help, I just need help with #2 now and I should be good. (Happy)
• Jan 12th 2010, 05:48 AM
Prove It
Quote:

Originally Posted by Lokith
Thanks for the help, I just need help with #2 now and I should be good. (Happy)

What you have posted in Q.2 is not a function of $t$.

Double check it.