Simplify the expression. 22 • 23 A. 10 B.16 C.24 D.32

Help ASAP show work please thanksss!!!!

Llana [10]

Answer:

$\displaystyle log_\frac{1}{2}(64)=-6$

Step-by-step explanation:

Properties of Logarithms

We'll recall below the basic properties of logarithms:

$log_b(1) = 0$

Logarithm of the base:

$log_b(b) = 1$

Product rule:

$log_b(xy) = log_b(x) + log_b(y)$

Division rule:

$\displaystyle log_b(\frac{x}{y}) = log_b(x) - log_b(y)$

Power rule:

$log_b(x^n) = n\cdot log_b(x)$

Change of base:

$\displaystyle log_b(x) = \frac{ log_a(x)}{log_a(b)}$

Simplifying logarithms often requires the application of one or more of the above properties.

Simplify

$\displaystyle log_\frac{1}{2}(64)$

Factoring $64=2^6$ .

$\displaystyle log_\frac{1}{2}(64)=\displaystyle log_\frac{1}{2}(2^6)$

Applying the power rule:

$\displaystyle log_\frac{1}{2}(64)=6\cdot log_\frac{1}{2}(2)$

Since

$\displaystyle 2=(1/2)^{-1}$

$\displaystyle log_\frac{1}{2}(64)=6\cdot log_\frac{1}{2}((1/2)^{-1})$

Applying the power rule:

$\displaystyle log_\frac{1}{2}(64)=-6\cdot log_\frac{1}{2}(\frac{1}{2})$

Applying the logarithm of the base:

$\mathbf{\displaystyle log_\frac{1}{2}(64)=-6}$

5 0

2 years ago

Graph Y= 1/3x {If someone could help me on this I would really appreciate it}

gizmo_the_mogwai [7]

Y=1/3x while m=0................

.
.
......

7 0

2 years ago

Read 2 more answers

The number of hours per week that the television is turned on is determined for each family in a sample. The mean of the data is

Zigmanuir [339]

I don’t know skip that question

7 0

2 years ago

TV studio has brought in 9 boy kittens and 6 girl kittens for a cat food commercial. The director is going to choose 9 of these

Amanda [17]

Answer:

probability = 0.2517

Step-by-step explanation:

given data

boy kittens = 9

girl kittens = 6

choose kittens at random = 9

solution

total kitten are = 9 + 6 = 15

first we get here total no of probability that is

n(s) = 15 C 9

n(s) = $\frac{15!}{9!(15-9)!}$

n(s) =5005

and

total way to chose 5 boy kittens is = 9 C 3

n(3) = $\frac{9!}{3!(9-3)!}$

n(3) = 84

and

total way to chose 4 girl kittens is = 6 C 4

n(4) = $\frac{6!}{4!(6-4)!}$

n(4) = 15

so

total way to chose 5 boy kittens and 4 girl kittens is

total way = 84 ×15 = 1260

so probability that the director chooses 5 boy kittens and 4 girl kittens is

probability = $\frac{1260}{5005}$

probability = 0.2517

6 0

3 years ago

Which is the graph of the function f(x) = -√x?

Virty [35]

Answer:

Step-by-step explanation:

The last (fourth) graph is that of the parent function y = √x. The negative sign in front of √x leads to reflection of this parent function graph in the x-axis. Thus, the correct graph of f(x) = -√x is the first one.

7 0

2 years ago