4. solve
e) 4^x-10.2^x+16=0
I think the dot means multiply?

Answers

Answer 1

Answer: $4^x-10\cdot2^x+16=0\Rightarrow(2^2)^x-10\cdot2^x+16=0\Rightarrow(2^x)^2-10\cdot2^x+16=0$

$subtitute\ 2^x=t > 0\n\nt^2-10t+16=0\nt^2-2t-8t+16=0\nt(t-2)-8(t-2)=0\n(t-2)(t-8)=0\iff t-2=0\ or\ t-8=0\n\nt=2\ or\ t=8\n\nt=2^1\ or\ t=2^3\n\ntherefore\ 2^x=2^1\ or\ 2^x=2^3\n\nAnswer:\boxed{x=1\ or\ x=3}$

Answer 2

Answer: 2^x=a
4^x=(2^2)^x=(2^x)^2=a^2

a^2-10a+16=0
Δ=10^2-4*1*16=100-64=36
√Δ=6
a1=(10+6)/2=16/2=8
a2=(10-6)/2=4/2=2
2^x=8=2^3⇒ x=3 or
2^x=2=2^1⇒ x=1

There are 2 solutions : x=1 or x=3

Related Questions

What is the half of 15
Is it possible to write a sequence that is both arithmetic and geometric
Caisha has a circular garden with a radius of 4 ft. She needs to put a layer of soil on top. Each bag of soil covers 9.42 square feet. How many bags of soil will she need to buy? 5 bag 6 bags 7 bags 8 bags
Pls solve this ASAPFind h(height)
Write the number in two other form 0.326I

Which of the following is the parent function of all absolute value functions?f(x) = 3x
f(x) = |x|
f(x) = 2|x|
f(x)=x^2

Answers

Hello,

The parent function of all absolute value functions is the f(x) = |x|.
I'll explain why.
f(x) = 3x is a linear function.
f(x) = 2|x| is an absolute value function, but it has a vertical stretch by a factor of 2, and we want to find the parent function, it needs to be in the most simplest form.
f(x) = x² is a quadratic function.

So, the final answer is choice 2, f(x) = |x|.

Answer:

Step-by-step explanation:

I took the test

After the stock market crash, the government created the ______to regulate businesses.A. Stock Market Oversight Board B. Internal Revenue Service C. Business Administration Commission D. Securities and Exchange Commission

Answers

Answer:

D the sec

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hope this helps!! Good luck!!!

What multiplies to equal 50, but adds to equal 12?

Answers

5 because 5x10=50 and 7+5=12

Nothing. If you are factoring you are going to need to use the quadratic formula for this problem.

Factorization of x²-5x-36

Answers

Answer

(x+4) x (x-9)

Use an online calculator to answer questions like this-

Photo-Math is a good app

How many pairs of intersecting line segment does a square have

Answers

it has four intersecting line segments lol

The probability that a random variable is greater than or equal to z standard deviations from the mean in a standard normal distribution is p%. What can be said with certainty about the probability that the random variable is less than or equal to –z standard deviations from the mean?