contestada

−6⋅20.1x=−100

Which of the following is the solution of the equation?
Choose 1 answer:
Choose 1 answer:

(Choice A)
A
x
=
2
(
50
)
2
(
3
)
x=
log
2

(3)
log
2

(50)

x, equals, start fraction, log, start base, 2, end base, left parenthesis, 50, right parenthesis, divided by, log, start base, 2, end base, left parenthesis, 3, right parenthesis, end fraction

(Choice B)
B
x
=
10
2
(
50
3
)
x=10log
2

(
3
50

)x, equals, 10, log, start base, 2, end base, left parenthesis, start fraction, 50, divided by, 3, end fraction, right parenthesis

(Choice C)
C
x
=
10
2
(
50
)
2
(
3
)
x=
log
2

(3)
10log
2

(50)

x, equals, start fraction, 10, log, start base, 2, end base, left parenthesis, 50, right parenthesis, divided by, log, start base, 2, end base, left parenthesis, 3, right parenthesis, end fraction

(Choice D)
D
x
=
2
(
50
3
)
x=log
2

(
3
50

)x, equals, log, start base, 2, end base, left parenthesis, start fraction, 50, divided by, 3, end fraction, right parenthesis

6201x100 Which of the following is the solution of the equation Choose 1 answer Choose 1 answer Choice A A x 2 50 2 3 x log 2 3 log 2 50 x equals start fraction class=

Respuesta :

Answer:

The answer (D)

x=log2(50/3)

Thus, [tex]x=10log_{2}\frac{50}{3}[/tex] so option (B) is the correct answer.

What is a logarithm?

"A logarithm tells what exponent (or power) is needed to make a certain number, so logarithms are the inverse (opposite) of exponentiation. Just as an exponential function has three parts, a logarithm has three parts as well: a base, an argument, and an answer (also called power)".

For the given situation,

The equation is

[tex]-6(2)^{0.1x} = -100[/tex]

The equation can be expressed in logarithm as

[tex]a^{x}=b\\[/tex]

⇒ [tex]x=log_{a}b[/tex]

So, [tex]-6(2)^{0.1x} = -100[/tex]

⇒ [tex]2^{0.1x}=\frac{-100}{-6} \\[/tex]

⇒ [tex]0.1x=log_{2}\frac{50}{3}[/tex]

⇒[tex]\frac{1}{10}x=log_{2} \frac{50}{3}[/tex]

⇒[tex]x=10log_{2}\frac{50}{3}[/tex]

Hence we can conclude that [tex]x=10log_{2}\frac{50}{3}[/tex]  option (B) is the correct answer.

Learn more about logarithm here

https://brainly.com/question/11848120

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