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m_a_m_a [10]
3 years ago
9

Which logarithmic equation is equivalent to this exponential equation? 12=5^x

Mathematics
1 answer:
Brut [27]3 years ago
5 0

Given:

The equation is:

12=5^x

To find:

The logarithmic equation that is equivalent to the given exponential equation.

Solution:

According to the property of logarithm:

a=b^x\Leftrightarrow \log_b a=x

We have,

12=5^x

Here, a=12,b=5. By using the above property of logarithm, we get

\log_{5}12=x

x=\log_{5}12

Therefore, the correct option is C.

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A superhero is trying to leap over a tall building. The function f(x)=-16x^2+200x gives the superhero's height in feet as a func
Gemiola [76]

Answer:

Since \bigtriangleup \geq 0, the superhero makes it over the building.

Step-by-step explanation:

The height is given by the following function:

f(x) = -16x^{2} + 200x

Will the superhero make it over the building?

We have to find if there is values of x for which f(x) = 612.

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

ax^{2} + bx + c, a\neq0.

This polynomial has roots x_{1}, x_{2} such that ax^{2} + bx + c = a(x - x_{1})*(x - x_{2}), given by the following formulas:

x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}

x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}

\bigtriangleup = b^{2} - 4ac

If \bigtriangleup < 0, the polynomial has no solutions.

In this question:

f(x) = -16x^{2} + 200x

-16x^{2} + 200x = 612

16x^{2} - 200x + 612 = 0

We have to find \bigtriangleup

We have that a = 16, b = -200, c = 612. So

\bigtriangleup = (-200)^{2} - 4*16*612 = 832

Since \bigtriangleup \geq 0, the superhero makes it over the building.

7 0
3 years ago
At the beginning of the month a store had a balance of −$554. During the month the store lost another $600. What is the current
musickatia [10]
 When subtracting a number from a negative number the number appears to get larger, but in fact only becomes smaller. - 554 - 600 = - $1154
4 0
3 years ago
Read 2 more answers
Help me! I need to finish these questions quickly!!!!
goldfiish [28.3K]

Answer:

18

Step-by-step explanation:

4 0
2 years ago
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Elliot has a total of 26 books. He has 12 more fiction books than nonfiction books. Let x represent the number of fiction books
Llana [10]
X and y are books
x is fiction
y=nonifiction

x+y=36


x=12+y

12+y+y=26
2y+12=26
minus 12
2y=14
divide 2
y=7


sub
x=12+y
x=12+7
x=19

nonfiction=7
5 0
3 years ago
the graph below shows the relationship between dithering distances a delivery truck is driven and the amount of gas the truck us
LiRa [457]

Answer:

10

Step-by-step explanation:

Look at where the one gallon gas is, it's point comes to ten. :)

4 0
2 years ago
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