Question

f a^b = b^c = ab, then b + c always equals (1) 1/ bc (2) 1 /2 bc (3) 1 (4) bc

Answer 1

If a^b = b^c = ab, then b + c will always be bc

Step-by-step explanation:

Let

P = a^b = b^c = ab

⇒ a^b = P

Now, by taking the log, we get

⇒ b log a = log P     ...(i)

∵ b^c  = P

by taking the log again, we get

⇒ c log b = log P       ...(ii)

∵ ab = P

By taking log, we get

⇒ log a + log b = log P

Through equations (i) & (ii), it can be said that

⇒ log P/b + log P/c = log P

⇒ 1/b + 1/c = c

∵ b + c = bc

Thus, option 4 is the correct answer.

Learn more: Find the value of log ⁴₃. log⁵₄. log₅⁶.log ⁷₆.log⁸₇.log⁹₈

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