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3 years ago

What is the value of n in the equation shown below? 2^2 x 2^n = (2^4)^3

1 answer:

3 0

So 2^2*2^n=(2^4)^3
2^2= 4
2^4=16
Then 16^3=4096
Now what we have is 4*2^n= 4096
You need to get the 2^n by itself so divide out the 4
4096/4= 1024
2^n=1024
Now you need to do log to get rid of that exponent
Therefore: n=log2(2024) or n=10

ANSWER
n=10

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Answer:

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Step-by-step explanation:

Given exponential function:

$f(x)=3(5)^x$

The growth factor between $x=1$ and $x=3$ is 25.

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Solution:

The growth factor of an exponential function in the interval $x=a$ and $x=b$ is given by :

$G=\frac{f(b)}{f(a)}$

We can check this by plugging in the given points.

The growth factor between $x=1$ and $x=3$ would be calculated as:

$G=\frac{f(3)}{f(1)}$

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$f(1)=3(5)^1$

Plugging in values.

$G=\frac{3(5)^3}{3(5)^1}$

$G=\frac{(5)^3}{(5)^1}$ (On canceling the common terms)

$G=(5)^{(3-1)}$ (Using quotient property of exponents $\frac{a^b}{a^c}=a^{(b-c)}$ )

$G=(5)^{2}$

∴ $G=25$

Similarly the growth factor between $x=5$ and $x=7$ would be:

$G=\frac{f(7)}{f(5)}$

$f(7)=3(5)^7$

$f(5)=3(5)^5$

Plugging in values.

$G=\frac{3(5)^7}{3(5)^5}$

$G=\frac{(5)^7}{(5)^5}$ (On canceling the common terms)

$G=(5)^{(7-5)}$ (Using quotient property of exponents $\frac{a^b}{a^c}=a^{(b-c)}$ )

$G=(5)^{2}$

∴ $G=25$

Thus, the growth factor remains the same which is =25.

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