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3 years ago

Express 125 = 5x as a logarithmic equation.

1 answer:

3 0

Answer: x log[5] = log[125]

Explanation:

The original expression is 125 = 5^x

To express that as a logarithmic equation take logarithms on both sides:

log [125] = [log 5^x]

By the properties of the logartims of powers that is:

log [125] = x log[5]

And that is the equation required.

If you want to solve it, you can do 125 = 5^2, and apply the same property (logarithm of a power) to the left side, yielding to:

log [5^2 ]= x log[5]

=> 2 log[5] = x log[5]

=> 2 = x

You might be interested in

How many 5-member chess teams can be chosen from 15 interested players? Consider only the members selected, not their board posi

ryzh [129]

<u>Answer</u>:

3003 number of 5-member chess teams can be chosen from 15 interested players.

<u>Step-by-step explanation:</u>

Given:

Number of the interested players = 15

To Find:

Number of 5-member chess teams that can be chosen = ?

Solution:

Combinations are a way to calculate the total outcomes of an event where order of the outcomes does not matter. To calculate combinations, we will use the formula $nCr = \frac{n!}{r!(n - r)!}$

where

n represents the total number of items,

r represents the number of items being chosen at a time.

Now we have n = 15 and r = 5

Substituting the values,

$15C_5 = \frac{15!}{5!(15- 5)!}$

$15C_5 = \frac{15!}{5!(10)!}$

$15C_5 = \frac{15\times \times 14 \times 13 \times 12 \times 11 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 }{5 \times 4 \times 3 \times 2 \times 1(10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1)}$

$15C_5 = \frac{15\times \times 14 \times 13 \times 12 \times 11}{(5 \times 4 \times 3 \times 2 \times 1)}$

$15C_5 = \frac{360360}{120}$

$15C_5 = 3003$

7 0

3 years ago

__ years will be spent on sleeping and __ years will be spent on watching tv.

Contact [7]

Answer:

Sleeping looks to be at least 26 years and TV would be 9 years

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

120 A particular telephone number is used to receive both voice calls and fax messages. Suppose that 25% of the incoming calls i

seropon [69]

Answer:

a)0.5611

b)0.1828

c)0.6217

d)0.4389

e)6.25

Step-by-step explanation:

Let's define the following event :

X : ''Calls involving a fax message''

The random variable X can be modeled as a Binomial random variable.

N ~ Bi(n,p)

N ~ Bi(25,0.25)

Where n is the sample and p is the success probability

Let's also define nCr as the combinatorial number :

$nCr=\frac{n!}{r!(n-r)!}$

The probability function for X is :

$P(X=k)=nCk.p^{k}.(1-p)^{n-k}$

Where k is the number of success

a) $P(X\leq 6)$

$P(X\leq 6)=P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)+P(X=5)+P(X=6)$

$P(X\leq 6)=0.5611$

b) $P(X=6)=25C6.(0.25)^{6}.(1-0.25)^{19}=0.1828$

c) $P(X\geq 6)=1-P(X$

d) $P(X>6)=1-P(X\leq 6)=1-0.5611=0.4389$

e) They are asking us about the expected value for random variable X

In a Binomial random variable :

E(X) = μ = n.p

$E(X)=25(0.25)=6.25$

6 0

3 years ago

Compare 8.25 and 8.250

GenaCL600 [577]

The answer is = because of you take away the 0 in the decimal 8.250 it's the same decimal as 8.25 and in decimals the zeros farthest to the right don't matter.
8.25 = 8.250

3 0

3 years ago

a rectangle 24 meters long has the same area as a square with 12 meter sides. what are the dimensions of the rectangle?

Komok [63]

The dimensions of the rectangle are 24*6 meters

5 0

4 years ago