answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
LuckyWell [14K]
1 year ago
10

Explain how to solve 4^x+3 = 7 using the change of base formula log base b of y equals log y over log b. Include the solution fo

r x in your answer. Round your answer to the nearest thousandth.
Mathematics
1 answer:
Masja [62]1 year ago
7 0

The value of x is 1

Explanation:

The equation is 4^x+3=7

Subtracting both sides by 3, we get,

4^x=4

Taking log on both sides, we get,

\log 4^{x}=\log 4

Rewriting the equation by 4^{x}=u

Thus, we have,

\log u=\log 4

Applying log rule, if \log f(x)=\log g(x), then f(x)=g(x)

Thus, u=4

Substituting u=4 in 4^{x}=u, we get,

4^x=4

Also, since, a^{f(x)}=a^{g(x)}, then f(x)=g(x)

Thus, x=1

Hence, the value of x is 1

You might be interested in
A. One day Annie weighed 24 ounces more than Benjie, and Benjie weighed 3 1/4 pounds less than Carmen. How did Annie’s and Carme
Debora [2.8K]
<h2>Answer:</h2>

A.

Let Annie's weight be = a

Let Benjie's weighs = b

Let Carmen's weight be = c

One day Annie weighed 24 ounces more than Benjie, equation forms:

a=b+24        ......(1)

Benjie weighed 3 1/4 pounds less than Carmen.  

In ounces:

1 pound = 16 ounces

\frac{13}{4} pounds = \frac{13}{4}\times16=52 ounces

b=c-52  or

c=b+52    ......(2)

Now adding (1) and (2), we get

a+b=b+24+c-52

=> a=c-28

This gives  Annie weighs 28 ounces less than Carmen.

B.

We cannot know anyone's actual weight, as we only know their relative weights.

3 0
1 year ago
A salad made such that the difference between twice the ounces of greens and the ounces of carrots is at least 3. Also, the sum
kap26 [50]

Answer:

3rd graph down

Step-by-step explanation:

greens are x and carrots are y in my equations

2x - y >= 3

x + 2y < 4

The first equation is solid and will highlight everything to the right of it because it is a >

the second is dashed and will highlight everything to the left of it because it is a <

the only 2 graphs that show this are 1 and 3

looking at the points you can see that the points for the solid line are both the same so ignore those and go to the dashed lined ones.

on the first graph the points are (0,4)

plugging those into our equation gives us 0 + 2*4 <4

or 8<4 which doesnt make sense making 3 the correct graph

(sorry my answer wasnt posting so i had to start over and make it less detailed, but comment if you need any explanation)

4 0
2 years ago
Read 2 more answers
The Diagram shows a polygon composed of rectangles
Igoryamba

To find perimeter you add up all the sides so the answer is 210

8 0
1 year ago
Read 2 more answers
A survey of the men in a certain town showed that 35% of the men have blond hair and 14% of them have blond hair and blue eyes.
natita [175]
If you are given he has blond hair, so the total probability will be 35%. And among them, he needs to have blue eyes, its probability is 14% among the 35%. So the final probability is 14%/35%=40%.
7 0
2 years ago
30 POINTS!!! Jade decided to rent movies for a movie marathon over the weekend. The function g(x) represents the amount of money
Airida [17]

Answer:

B. No the input is not feasible

because you cannot rent 6,5 movies  :p

6 0
1 year ago
Read 2 more answers
Other questions:
  • If 2x+z=2y and 2x+2y+z=20 what is the value of y?
    11·1 answer
  • A construction crew is lengthening a road. The road started with a length of 54 miles, and the crew is adding 3 miles to the roa
    10·1 answer
  • The velocity of a ball is thrown up is 20 meters/second. It attains zero velocity after 3.5 seconds. What is the average acceler
    12·2 answers
  • I need help with this
    14·1 answer
  • Points C and D divide the semicircle into three equal parts. Match the angles with their measures.
    15·2 answers
  • If mBC = (9x-53) and mCD = (2x + 45) find mBAD
    9·1 answer
  • What are the domain and range of f (x) = (one-fifth) Superscript x?
    13·2 answers
  • Y=3x+5=<br> what is the slope
    15·1 answer
  • How many significant figures in 20340 ?
    12·2 answers
  • Dave's gas powered snow blower requires 3.5 ounces of oil to be mixed with every gallon of gasoline for fuel. If he is to add 4.
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!