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lidiya [134]
3 years ago
8

Explain how to solve 3^x-4=6 using the change of base formula log base b of y equals log y over log b. include the solution for

x in your answer. Round your answer to the nearest thousandth.
Mathematics
1 answer:
Alexxandr [17]3 years ago
7 0

Answer:

x = log 10/log 3

Step-by-step explanation:

3^x - 4 = 6

3^x = 10

We take log base 3 of both sides since log_3 3^x is simply x.

log_3 3^x = log_3 10

x = log_3 10

We have an answer for x, but it is a log base 3. We want log base 10.

Now we use the change of base formula.

log_b y = log y/log b

x = log 10/log 3

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A rectangular cake has a length of 22 1/2 inches and a width of 10 inches. How many whole, square pieces of cake with side lengt
faltersainse [42]
Well, we need to find the area of the cake.  22.5 times 10 is 225.  That is the area then we need to find the area of each piece of cake.  2.5 times 2.5 is 6.26.
so divide the area of the cake by the area of each piece to find how many pieces can be cut.
225/6.25=36  36 pieces of cake can be cut from the cake
5 0
3 years ago
34. Lora is thinking of a number. It is less than 50 It is a 2-digit number. 3 is a factor of this number. The sum of its digits
-Dominant- [34]

Answer:

B

Step-by-step explanation:

The number is between 10 and 49

The number is divisible by 3

Let the 10s digit = x

Let the units digit = y

1/3 * (10x + y)  = x + y          multiply both sides by 3

10x + y = 3(x +y)                  remove the brackets.

10x +y = 3x + 3y                  Subtract 3x from both sides

10x - 3x + y = 3y                  Combine\

7x + y = 3y                           Subtract y from both sides.

7x = 3y - y                           Combine

7x = 2y

x can't be very big. Even taking 1/3 will get out of range is you use 6.

Also x should be an even number. The units digit cannot have a fraction in it.

Try making x = 2

7*2 = 2*y

14 = 2y                                Divide by 2

14/2 = y

y = 7

So the number is possibly 27. Let's check it out.

  • The number is between and includes 10 and 49. 27 is between these two endpoints.
  • 27 is divisible by 3
  • 1/3(27) = sum of digits
  • 9 = (2 + 7)

All of the conditions are met. It's B

8 0
2 years ago
What values of b satisfy 3(2b+3)^2 = 36
Maslowich
\frac{-3 +/- 2 \sqrt{3} }{2}

Start by dividing both sides by 3. Then take the square root of both sides. Then subtract 3 from both sides and divide by 2.  
5 0
3 years ago
Read 2 more answers
What is the nth term of this sequence below?   <br><br> 2, 5, 8, 11 , 14. ......etc.
Gemiola [76]
The nth term is 26 because each number is being added by 3. for example: 2+3=5, 5+3=8, etc.
5 0
3 years ago
JK has endpoints at -12 and 4. What is the coordinate of its midpoint
iris [78.8K]

Answer:

- 4

Step-by-step explanation:

Midpoint of JK

=  \frac{ - 12 + 4}{2}  \\  \\  =  \frac{ - 8}{2}  \\  \\  =  - 4

7 0
3 years ago
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