1answer.
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
blsea [12.9K]
3 years ago
15

3,125=5^-10+3x What does x equal

Mathematics
2 answers:
earnstyle [38]3 years ago
8 0

Answer:

x = 30517578124/29296875

Step-by-step explanation:

Solve for x:

3125 = 3 x + 1/9765625

Put each term in 3 x + 1/9765625 over the common denominator 9765625: 3 x + 1/9765625 = (29296875 x)/9765625 + 1/9765625:

3125 = (29296875 x)/9765625 + 1/9765625

(29296875 x)/9765625 + 1/9765625 = (29296875 x + 1)/9765625:

3125 = (29296875 x + 1)/9765625

3125 = (29296875 x + 1)/9765625 is equivalent to (29296875 x + 1)/9765625 = 3125:

(29296875 x + 1)/9765625 = 3125

Multiply both sides of (29296875 x + 1)/9765625 = 3125 by 9765625:

(9765625 (29296875 x + 1))/9765625 = 9765625×3125

(9765625 (29296875 x + 1))/9765625 = 9765625/9765625×(29296875 x + 1) = 29296875 x + 1:

29296875 x + 1 = 9765625×3125

9765625×3125 = 30517578125:

29296875 x + 1 = 30517578125

Subtract 1 from both sides:

29296875 x + (1 - 1) = 30517578125 - 1

1 - 1 = 0:

29296875 x = 30517578125 - 1

30517578125 - 1 = 30517578124:

29296875 x = 30517578124

Divide both sides of 29296875 x = 30517578124 by 29296875:

(29296875 x)/29296875 = 30517578124/29296875

29296875/29296875 = 1:

Answer:  x = 30517578124/29296875

OlgaM077 [116]3 years ago
4 0

For this case:

We rewrite the equation as:

5 ^ {- 10 + 3x} = 3.125

We find ln on both sides of the equation to remove the exponent variable:

ln (5 ^ {- 10 + 3x}) = ln (3,125)

Applying properties of logarithm we have:

(-10 + 3x) ln (5) = ln (3.125)

We apply distributive property:

-10ln (5) + 3xln (5) = ln (3,125)

We clear the value of "x":

3xln (5) = ln (3,125) + 10ln (5)\\x = \frac {ln (3.125)} {3ln (5)} + \frac {10ln (5)} {3ln (5)}\\x = \frac {ln (3.125)} {3ln (5)} + \frac {10} {3}

ANswer:

x = \frac {ln (3.125)} {3ln (5)} + \frac {10} {3}

You might be interested in
Help me asap!!! <br><br> 3(m+7) = 6 (m+2)
siniylev [52]

Answer:

m=3

Step-by-step explanation:

3 0
2 years ago
HELP ME PLZ!!!!! Identify the domain of the graph of y = −x2 − 6x − 13. (1 point) All real numbers x ≤ −4 x ≥ −6 x ≥ −2
vlada-n [284]

Answer:

Step-by-step explanation:

All real numbers because x can assume every possible value

5 0
2 years ago
Read 2 more answers
If f(x) = 4(3x - 5), find f-1(x)
deff fn [24]

Answer:

f^{-1}(x) =  \frac{1}{12}(x+20)

Step-by-step explanation:

Given: f(x) = 4(3x - 5)

Is required to find f⁻¹(x)

f(x) = y = 4(3x - 5)

∴ y = 4 * 3x - 4 * 5

∴ y = 12x - 20 ⇒ add 20 to both sides

∴ y + 20 = 12x ⇒ divide both sides by 12

∴ \frac{1}{12} (y+20) = x

Replace the places of x and y.

∴ y=\frac{1}{12} (x+20)

∴ f^{-1}(x) =  \frac{1}{12}(x+20)

7 0
3 years ago
3/5 divided by 2 and 1/2
REY [17]

Step-by-step explanation:

6/10

divided by 2

3/10

divided by 1/2

3/5

4 0
3 years ago
Matthew's dad is 5 times as old as him. If the differences of their ages is 28, how old is matthew?
enyata [817]

Answer:

7

Step-by-step explanation:

5x-x=28  The dad is 5 times as old and the difference in their ages is 28years.

4x=28 Simplify and divide.

x=7

6 0
2 years ago
Other questions:
  • Which equation is equivalent to 4s=t+2
    5·1 answer
  • 3.3 greater than or less than 0.33​
    5·2 answers
  • It took Jen, who biked at a speed of 12 mph, 20 minutes to get home. What is Jim’s speed, if it took him only 15 minutes to bike
    5·1 answer
  • 9x two the second power = 1
    15·2 answers
  • A meal at a restaurant cost $ 22 and the sale tax of $ 1.87 was added to the bill. what is sale tax in this city?​
    8·1 answer
  • Please help me ASAP.
    5·2 answers
  • Which points on the number line are 8 units away from 0?
    11·2 answers
  • Whats the solution to 2/3x^2+24
    15·1 answer
  • Given the equation 5x + 3y = 15, which statement is true?
    15·1 answer
  • What is the least common multiple of 3, 17, and 51?
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!