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3 years ago

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Mathematics

1 answer:

natka813 [3]3 years ago

3 0

Answer:

Show the figure

Step-by-step explanation:

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Solve for x write the exact answer using either base -10 or base-e logarithms

jeka57 [31]

<u>Given</u>:

The given expression is $2^{x+5}=13^{2 x}$

We need to determine the value of x using either base - 10 or base - e logarithms.

<u>Value of x:</u>

Let us determine the value of x using the base - e logarithms.

Applying the log rule that if $f(x)=g(x)$ then $\ln (f(x))=\ln (g(x))$

Thus, we get;

$\ln \left(2^{x+5}\right)=\ln \left(13^{2 x}\right)$

Applying the log rule, $\log _{a}\left(x^{b}\right)=b \cdot \log _{a}(x)$ , we get;

$(x+5) \ln (2)=2 x \ln (13)$

Expanding, we get;

$x \ln (2)+5 \ln (2)=2 x \ln (13)$

Subtracting both sides by $5 \ln (2)$ , we get;

$x \ln (2)=2 x \ln (13)-5 \ln (2)$

Subtracting both sides by $2 x \ln (13)$ , we get;

$x \ln (2)-2 x \ln (13)=-5 \ln (2)$

Taking out the common term x, we have;

$x( \ln (2)-2 \ln (13))=-5 \ln (2)$

$x=\frac{-5 \ln (2)}{\ln (2)-2 \ln (13)}$

$x=\frac{5 \ln (2)}{2 \ln (13)-\ln (2)}$

Thus, the value of x is $x=\frac{5 \ln (2)}{2 \ln (13)-\ln (2)}$

6 0

3 years ago

How many times greater is 3400 than 340

Lelu [443]

3400 is 10 times greater than 340 because if you divide 3400 by 10, you will get 340. Letting you know that 3400 is 10(ten) times greater than 340.

3 0

3 years ago

Read 2 more answers

Which expression is equivalent to 7/4?

arsen [322]

Answer:

1 3/4

Step-by-step explanation:

improper to mixed number

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3 years ago

What numbers make the product of 17? None?

skad [1K]

Answer:

there is no Pairs that equal 17

Step-by-step explanation:

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2 years ago

Choose the correct problem formulation: Hotels, like airlines, often overbook, counting on the fact that some people with reserv

Marina CMI [18]

Answer:

$P(8 < x \leq 12)=P(X=9)+P(X=10)+P(X=11)+P(X=12)$

$P(X=9)=(15C9)(0.8)^{9} (1-0.8)^{15-9}=0.0429$

$P(X=10)=(15C10)(0.8)^{10} (1-0.8)^{15-10}=0.1032$

$P(X=11)=(15C11)(0.8)^{11} (1-0.8)^{15-11}=0.1878$

$P(X=12)=(15C12)(0.8)^{12} (1-0.8)^{15-12}=0.2501$

$P(8 < x \leq 12)=0.0429+0.1032+0.1878 +0.2501=0.5839$

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=15, p=1-0.2=0.8)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

And we want to find this probability:

$P(8 < x \leq 12)=P(X=9)+P(X=10)+P(X=11)+P(X=12)$

$P(X=9)=(15C9)(0.8)^{9} (1-0.8)^{15-9}=0.0429$

$P(X=10)=(15C10)(0.8)^{10} (1-0.8)^{15-10}=0.1032$

$P(X=11)=(15C11)(0.8)^{11} (1-0.8)^{15-11}=0.1878$

$P(X=12)=(15C12)(0.8)^{12} (1-0.8)^{15-12}=0.2501$

$P(8 < x \leq 12)=0.0429+0.1032+0.1878 +0.2501=0.5839$

7 0

3 years ago