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sweet-ann [11.9K]
3 years ago
14

If logb 5=0.41, find logb 12

Mathematics
1 answer:
Hitman42 [59]3 years ago
6 0
<span>Determine which one of the following is the correct application of the change of base formula?

a)log3 14= log10 14/3
b)lo4 17= log10 4/ log10 17
c)log8 3= log10 3/log10 8
d)log9 32 = log10 32-log10 9

The change of base formula is as follows:
                                         log to the base 10 of x
log to the base b of x  = ----------------------------------
                                          log to the base 10 of b

Compare this to answer choice C:

</span><span>c)log8 3= log10 3/log10 8      Here x = 3 and b = 8.  This is the only correct choice.</span><span>

</span>
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How would I do question 5 I don’t understand
bazaltina [42]

Answer:

a) f(0)=4

b) f(-2)=2

c) x∈{-8,-4,4,8}

d) x∈{-9,-3,3,9}

e) x∈(-∞,-9)∪(-3,3)∪(9,∞).

f)  x∈[-9,-3]∪[3,9]

g) Domain is x∈[-10,10]. Range is y∈[-4,4]. Zeros are at elements of x in {-9,-3,3,9}

h) Increasing on x∈ (-6,0) ∪ (6,10) and

decreasing on x∈ (-10,-6) ∪ (0,6).

Step-by-step explanation:

a) f(0) means what is the y-coordinate of the point at x=0.

So find 0 on the x-axis. I'm going to go up because the curve is at y=4 there.

Conclusion: f(0)=4.

b) f(-2) means what is the y-coordinate of the point at x=-2.

So find -2 on the x-axis. I'm going to go up because the curve is at y=2 there.

Conclusion:  f(-2)=2.

c) f(x)=-2 means what is x when y=-2.  So go on the y-axis and find -2. Now anything on that line y=-2 (horizontal line going through y=-2 on the y-axis) we need to look at.

There are 4 value we need to look at then.

x=-8

x=-4

x=4

x=8

At all of these the y-coordinate is -2.

d) f(x)=0 means what is x when y=0.  So go on the y-axis and find 0. Now anything on that line y=0 (horizontal line going through y=0 on the y-axis; also knowing as the x-axis for y=0) we need to look at.

There are 4 values we need to look at then.

x=-9

x=-3

x=3

x=9

e)  f(x)>0 means where is the curve above the x-axis.

The curve is above the x-axis:

  • Before x=-9
  • Between x=-3 and x=3
  • After x=9

The interval notation is:

(-∞,-9)∪(-3,3)∪(9,∞).

d) f(x)≥0 means where is the curve below or on the x-axis (also known as y=0).

The curve is below or on the x-axis:

  • Between -9 and -3 (inclusive of both endpoints because they include y=0).
  • Between 3 and 9 (inclusive of both endpoints because they include y=0).

The interval notation is:

[-9,-3]∪[3,9]

g) The domain is where the curve exists for the x-values.

The domain is all real numbers between -10 and 10 (inclusive of both).

The curve starts at x=-10 and stops at x=10. The function exists a y value for any number between -10 and 10 (including both).

Interval notation is:

[-10,10]

The range is where the curve exists for the y-values.

Looking from bottom to top I see that it starts at y=-4 and stops at y=4. I notice the curve exists at some point between those two horizontal lines. It also exists at both of those endpoints" -4 and 4.

The range is between -4 and 4 (including both).

Interval notation is:

[-4,4]

The zeros are where the graph crosses the x-axis.

The graph crosses the x-axis at:

x=-9

x=-3

x=3

x=9

h)  Reading left to right the graph increases when you see the curve going up.

I see this from x=-6 to x=0 (exclusive of both).

I see this from x=6 to x=10 (exclusive of both).

So interval notation is (-6,0) ∪ (6,10).

Reading left to right the graph decreases when you see the curve going down.

I see this from x=-10 to x=-6 ( exclusive of both).

I see this from x=0 to x=6 (exclusive of both).

4 0
3 years ago
The sum of 8n²- 3n + 10 and 3n² - 6n-7 is ?​
vampirchik [111]

Step-by-step explanation:

= (8n² - 3n + 10) + (-3n² - 6n - 7)

= (8 - 3)n² + (-3 - 6)n + (10 - 7)

= 5n² - 9n + 3

Option → #1

5 0
2 years ago
Use the point slope equation to identify the slope and the coordinates of a point on the line y=1/2(x-1)
gtnhenbr [62]

Answer:

see explanation

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

y = \frac{1}{2}(x - 1) is in this form

with slope m = \frac{1}{2}

note left side of equation can be written as

y - 0 = \frac{1}{2}(x - 1)

the point on the line (a, b) = (1, 0)

8 0
3 years ago
Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
alexandr1967 [171]

The total cost of the bracelet will be $96.

The number of charms will be 2.

Step-by-step explanation:

Given,

Cost per charm at Dayton Fine Jewelry = $17

Cost of bracelet = $62

Let,

x be the number of charms

y be the total cost

y = 17x+62   Eqn 1

Cost per charm at Cain Jewelers = $18

Cost of bracelet = $60

y = 18x+60   Eqn 2

For same cost;

Eqn 1 = Eqn 2

17x+62=18x+60\\62-60=18x-17x\\2=x\\x=2

Putting x=2 in Eqn 1

y=17(2)+62\\y=34+62\\y=96

Putting x=2 in Eqn 2

y=18(2) +60\\y=36+60\\y=96

The total cost of the bracelet will be $96.

The number of charms will be 2.

Keywords: equation, addition

Learn more about addition at:

  • brainly.com/question/1021953
  • brainly.com/question/10480770

#LearnwithBrainly

4 0
3 years ago
Long division 25 dived by 2550
Elina [12.6K]

Answer:

25 divided by 2550 = 0.009803922

2550 divided by 25 = 102

Step-by-step explanation:


6 0
3 years ago
Read 2 more answers
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