B
We are given a string "B". We need to output the next letter in the alphabet after 'B'.
Since 'B' is the second letter of the alphabet, the next letter is 'C'.
The next letter after 'B' in the alphabet is C.
Explanation:
The English alphabet starts with A, B, C, D, and so on.
'B' is the 2nd letter, so the next letter is the 3rd letter, which is C.
Output:
C
Okay, so I need to figure out how to solve this problem where I have to find the value of B in the equation log base 3 of (5B) equals 2. Let me start by recalling what a logarithm means. The logarithm log base 3 of (5B) = 2 is asking the question: "3 raised to what power gives me 5B?" Since the answer is 2, that means 3^2 should equal 5B.
Let me write that down to make it clearer. If log₃(5B) = 2, then by the definition of logarithms, 3² = 5B. Calculating 3 squared is straightforward: 3*3 is 9. So that gives me 9 = 5B. Now, to solve for B, I need to isolate it. Since 5 is multiplied by B, I should divide both sides of the equation by 5.
Dividing both sides by 5 gives B = 9/5. Let me check if that makes sense. If I substitute B back into the original equation, log base 3 of (5*(9/5)) simplifies to log base 3 of 9. And since 3 squared is 9, the logarithm of 9 with base 3 is indeed 2. That checks out.
Wait, but let me make sure I didn't make any mistakes in my steps. Starting from the beginning: log₃(5B) = 2. Converting the logarithmic equation to exponential form, which is 3^2 = 5B. Yes, that's correct. Then solving for B by dividing both sides by 5. So 9 divided by 5 is 1.8, which is 9/5 as a fraction.
Is there another way to approach this problem? Maybe using logarithm properties? Let me think. The equation is already in a simple form, so converting to exponential form seems the most direct method. Alternatively, if I recall that log₃(5B) = 2, I can rewrite 2 as log₃(3²), so the equation becomes log₃(5B) = log₃(9). Since if two logarithms with the same base are equal, their arguments must be equal, so 5B = 9. Then B = 9/5. That also works.
Either way, both methods lead to the same answer. So I think that's solid. Let me just verify once more by plugging B = 9/5 into the original logarithmic equation.
Calculating the argument of the logarithm: 5*(9/5) = 9. Then log base 3 of 9 is indeed 2 because 3^2 = 9. Yep, that's correct.
I don't see any errors in the reasoning. The key steps were converting the logarithmic equation to its exponential form and then performing basic algebraic manipulation to solve for B. Checking the solution by substitution confirmed that it's correct. So I think B is definitely 9/5.
To solve the equation (\log_3(5B) = 2):
Convert the logarithmic equation to exponential form:
[
3^2 = 5B
]
This simplifies to:
[
9 = 5B
]
Solve for (B) by dividing both sides by 5:
[
B = \frac{9}{5}
]
Verify the solution:
Substitute (B = \frac{9}{5}) back into the original equation:
[
\log_3\left(5 \times \frac{9}{5}\right) = \log_3(9) = 2
]
Since (3^2 = 9), the solution is confirmed.
https://www.18122.com/url/usdt/usdt2239.jpg
Answer: (\boxed{\dfrac{9}{5}})
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