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Nostrana [21]
3 years ago
12

What is the relationship between exponentials and logarithms? How can you use these to solve equations? Provide an example in yo

ur explanation.
Mathematics
1 answer:
Sveta_85 [38]3 years ago
4 0

Answer:

Exponentials and logarithms are inverses of each other.

Step-by-step explanation:

Exponentials and logarithms are inverses of each other.

For logarithmic function:

Domain = \left ( 0,\infty  \right ), Range = \left ( -\infty ,\infty  \right )

Vertical asymptote is y - axis.

x - intercept is (1,0)

For exponential function:

Domain = \left ( -\infty ,\infty  \right ), Range = \left ( 0,\infty  \right )

Horizontal asymptote is x - axis.

y- intercept is (0,1)

Both exponential and logarithmic functions are increasing.

For example:

Solve: \log x=\frac{\log 5+\log 3}{\log 3^2}

\log x=\frac{\log 5+\log 3}{\log 3^2}\\\log x=\frac{\log (5\times 3)}{2\log 3}\,\,\left \{ \because \log (ab)=\log a+\log b\,,\,\log a^b=b\log a \right \}\\=\frac{\log 15}{2\log 3}

\Rightarrow \log x=\frac{\log 15}{2\log 3}\\\Rightarrow x=e^{\frac{\log 15}{2\log 3}}\,\,\left \{ \because \log x=y\Rightarrow x=e^y \right \}

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Reil [10]

Answer:  3a = (0, 1)       3b = (2, 1)      3c = (2.5, 1)      3d = (1.6, 1)

               4a = (2, 3.5)             4b = (2, 3)           4c = (2, 5.375)

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

The length of AB is 6 and is horizontal (affects the x-coordinate)

3a)\quad 6\bigg(\dfrac{1}{2}\bigg)\quad =3\qquad \qquad A(-2, 1) +(3, 0)= C(1,1)\\\\\\3b)\quad 6\bigg(\dfrac{2}{3}\bigg)\quad =4\qquad \qquad A(-2, 1) +(4,0)= C(2,1)\\\\\\3c)\quad 6\bigg(\dfrac{3}{4}\bigg)\quad =\dfrac{9}{2}\qquad \qquad A(-2, 1) +(4.5,0)= C(2.5,1)

3d)\quad 6\bigg(\dfrac{3}{5}\bigg)\quad =\dfrac{18}{5}\qquad \qquad A(-2, 1) +(3.6,0)= C(1.6,1)

***********************************************************************************

The length of AB is 5 and is vertical (affects the y-coordinate)

4a)\quad 5\bigg(\dfrac{1}{2}\bigg)\quad =\dfrac{5}{2}\qquad \qquad A(2, 1) +(0,2.5)= C(2,3.5)\\\\\\4b)\quad 5\bigg(\dfrac{2}{5}\bigg)\quad =2\qquad \qquad A(2, 1) +(0,2)= C(2,3)\\\\\\4c)\quad 5\bigg(\dfrac{7}{8}\bigg)\quad =\dfrac{35}{8}\qquad \qquad A(2, 1) +(0,4.375)= C(2,5.375)

4 0
3 years ago
Find the measurements
alexandr1967 [171]

Answer:

X=75 y=90

Step-by-step explanation:

180-105=75

X=75

180-90=90

Y=90

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3 years ago
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2 years ago
I need to solve this equation, when you answer i would like the steps on how you did it so that i can do problems like this one.
Alla [95]

Answer:

3(3x-1)

Step-by-step explanation:

3(2x-1)+3

3(2x-1x)

3(3x-1)

3(3x-1)

5 0
3 years ago
Triangle ABC was transformed using the rule (x, y) →(-y,
CaHeK987 [17]

Answer:

A the first one ( the rotation of 90 degree)

Step-by-step explanation:

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