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2 years ago

What equation is equivalent to 2^3^x =10

Mathematics

1 answer:

Tresset [83]2 years ago

6 0

Answer:

$log_2(10)$

Simplify the equation using logarithms.

$2^3x=10$

$log_1_0(2^3x)=log_1_0(10)$

log rule ⇩

$log_a(x^y)=y*log_a(x)$

move exponent out of log.

$x*log_1_0(2)=log_1_0(10)$

<em>isolate variable further</em>

$x*log_1_0(2)=log_1_0(10)$

$x=\frac{log_{10}(10)}{log_{10}(2)}$

formula for combining logs. ⇩

$\frac {log_b(x)}{log_b(a)}=log_a(x)$

the result ⇩

$x=log_2(10)$

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Anarel [89]

Answer:

The correct answer is option B.

Step-by-step explanation:

Two point form of the equation:

A line passing through the point (-1,6) with slope ,m = -3.

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3 years ago

13. Is the following the graph of a function? Why or why not?

Semenov [28]

No. To test whether a graph is a function or not you do the vertical line test where if a vertical line touches more than one point it is not a function

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3 years ago

Determine the vertical asymptote for the rational function f(x) = x - 4 over 2x - 3

k0ka [10]

Answer:

x = $\frac{3}{2}$

Step-by-step explanation:

Given

f(x) = $\frac{x-4}{2x-3}$

The denominator cannot be zero as this would make f(x) undefined.

Equating the denominator to zero and solving gives the value that x cannot be and if the numerator is non zero for this value then it is a vertical asymptote.

2x - 3 = 0 ⇒ 2x = 3 ⇒ x = $\frac{3}{2}$

Thus x = $\frac{3}{2}$ is the vertical asymptote

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3 years ago

Point R is the midpoint of line QS. R is located at (5, -7.5) S is located at (-1,-13) What is the location of Point Q?

Lisa [10]

Answer: ( 11, -2 )

Step-by-step explanation:

The mid point of a line is calculated using the formula:

M = ( $\frac{x_{1}+x_{2}}{2}$ , $\frac{y_{1}+y_{2}}{2}$ )

From the question , the mid point is already given , substituting , we have :

(5 , - 7.5 ) = ( $\frac{x-1}{2}$ , $\frac{y-13}{2}$ )

Equating the x component to x and the y component to y , we have

5 = $\frac{x-1}{2}$

x - 1 = 10

x = 11

Also

- 7.5 = $\frac{y-13}{2}$

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-15 + 13 = y

Therefore : y = -2

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3 years ago

If a 10 symbol sequence is sent through the channel,what is the probability that up to 3 symbols are in error out of the 10trans

lina2011 [118]

Answer: 0.171887

Step-by-step explanation:

Given that S0 and S1 are binary symbol of equal probabilty;

P(S0) = P(S1) = 0.5

This probability is a Binomial random variable of sequence Sn, where Sn counting the number of success in a repeated trials.

P(Sn =X) = nCx p^x (1-p)^(n-1)

Pr(at most 3) = P(0<= x <=3) = P(X=0) + 0) + P(X=1) + P(X=2) + P(X=3)

Since there are only 2 values that occur in sequence 0 and 1 ( or S0 and S1).Let the distribution be given by the sequence (0111111111),(1011111111),(11011111111),...(1111111110) for Sn= 1 is the sequence for 1 error.

10C0, 10C1, 10C2, and 10C3 is the number of sequences in value for X= 0, 1, 2, 3 having value 0 and others are 1. Let the success be p(S0)=0.5 and p(S1)= 0.5

P(0<= X <=3) = 10C0 × (0.5)^0 × (0.5)^10 + 10C1× (0.5)¹ × (0.5)^9 + 10C2 × (0.5)² × (0.5)^8 + 10C3(0.5)³(0.5)^7

= 1 × (0.5)^10 + 10 × (0.5)^10 + 45 × (0.5)^10 + 120 × (0.5)^10

=0.000977 + 0.00977 + 0.04395 + 0.11719

= 0.171887

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