(2501) ^(x+5) = 343^2x
To solve the equation (2501)^(x+5) = 343^(2x), we can take the logarithm of both sides. Let's use the natural logarithm:
ln((2501)^(x+5)) = ln(343^(2x))
Using the logarithmic property of exponents, we can bring down the exponents:
(x + 5) ln(2501) = 2x ln(343)
Now, let's isolate the x terms:
x ln(2501) + 5 ln(2501) = 2x ln(343)
Distribute the ln(2501) term:
x ln(2501) + 5 ln(2501) = 2x ln(343)
Simplify:
x ln(2501) - 2x ln(343) = -5 ln(2501)
Factor out x:
x ( ln(2501) - 2 ln(343) ) = -5 ln(2501)
Divide both sides by (ln(2501) - 2 ln(343)):
x = -5 ln(2501) / (ln(2501) - 2 ln(343))
Thus, x = -5 ln(2501) / (ln(2501) - 2 ln(343)).
Adamu pays for a cable in 15 equal monthly instalments of 3200 naira. How long will it take him to pay for the cable if he pays 4800 naira per month
If Adamu pays 3200 naira per month and has to pay a total of 15 equal monthly instalments, then he would have paid a total of 3200 * 15 = 48,000 naira.
If he wants to pay 4800 naira per month, we can divide the total amount of 48,000 naira by the monthly payment of 4800 naira to find out how many months it will take:
48,000 naira / 4800 naira per month = 10 months
Therefore, it will take Adamu 10 months to pay for the cable if he pays 4800 naira per month.
A girl covered a distance of j meters per 1 second. Find the distance she covered in z hours
To find the distance the girl covered in z hours, we first need to convert the hours into seconds.
Since there are 60 minutes in an hour and 60 seconds in a minute, there are a total of 60 * 60 = 3600 seconds in an hour.
Therefore, the distance covered in z hours is j meters/second * 1 second * z hours * 3600 seconds/hour = j * z * 3600 meters.
Hence, the girl covered a distance of j * z * 3600 meters in z hours.
Business partners adamu and micheal's own a business. The ratio of adamu's share to micheal is 11:9. If 2/3 of micheal's share is 72000 naira. Calculate the value if the business
Let's denote Adamu's share as A and Micheal's share as M.
From the given information, we know that A:M=11:9.
Also, 2/3 of Micheal's share (2/3 * M) is equal to 72000 naira.
To find the value of the business, we need to determine the total value of Adamu and Micheal's shares.
Let's set up equations to solve for A and M:
A/M = 11/9 ---- (Equation 1)
2/3 * M = 72000 ---- (Equation 2)
To solve this system of equations, we can rearrange Equation 1 to express A in terms of M:
A = 11/9 * M ---- (Equation 3)
Substitute Equation 3 into Equation 2:
2/3 * M = 72000
Multiply both sides by 3/2 to isolate M:
M = (72000) * (3/2) = 108000
Now substitute the value of M back into Equation 3 to solve for A:
A = 11/9 * (108000) = 132000
Therefore, Adamu's share (A) is 132000 naira, and Micheal's share (M) is 108000 naira.
The total value of the business is the sum of Adamu's and Micheal's shares:
Total value = Adamu's share + Micheal's share
= 132000 + 108000
= 240,000 naira
Thus, the value of the business is 240,000 naira.
Business partners adamu and micheal's own a business. The ratio of adamu's share to micheal is 11:9. If 2/3 of micheal's share is 72000 naira. What aduma share in naira
Let's denote Adamu's share as A and Micheal's share as M.
From the given information, we know that the ratio of Adamu's share to Micheal's share is 11:9, or A:M = 11:9.
We are also given that 2/3 of Micheal's share is 72000 naira, so (2/3)M = 72000.
To find Adamu's share (A), we can set up a proportion:
A/M = 11/9
Cross-multiplying, we have:
9A = 11M
From the second piece of information, we can solve for M:
(2/3)M = 72000
Multiplying both sides by 3/2:
M = 72000 * 3/2
M = 108000
Substituting this value of M into the proportion:
9A = 11(108000)
Simplifying:
9A = 1188000
Dividing both sides by 9:
A = 1188000/9
A = 132000
Therefore, Adamu's share (A) is 132000 naira.
To solve this exponential equation, we will begin by considering the bases of the exponents, which are 2501 on the left side and 343 on the right side.
Let's start by examining the bases. We can rewrite 343 as 7^3 because 7 * 7 * 7 = 343. Similarly, 2501 cannot be factored into a nice power, so we will leave it as it is for now.
Rewriting the equation, we have:
(2501)^(x + 5) = (7^3)^(2x)
We can simplify further by using the property of exponents, which states that (a^b)^c = a^(b * c). Applying this property:
(2501)^(x + 5) = 7^(3 * 2x)
Now we can simplify the right side:
(2501)^(x + 5) = 7^(6x)
Since the bases 2501 and 7 are different, we need to express them with the same base. The simplest common base for both 2501 and 7 is 7.
Let's rewrite 2501 as a power of 7:
2501 = 7^3.85 (approximately)
Substituting this back into the equation:
7^(3.85 * (x + 5)) = 7^(6x)
Now, we have the same base, so the exponents must be equal:
3.85 * (x + 5) = 6x
Let's simplify:
3.85x + 19.25 = 6x
Now, we can isolate the x term by subtracting 3.85x from both sides:
19.25 = 6x - 3.85x
Combining like terms:
19.25 = 2.15x
Finally, to solve for x, we can divide both sides by 2.15:
x ≈ 8.953
So the solution to the equation is approximately x ≈ 8.953.