perplexus.info :: Just Math : Find the value of a*b*c*d

Find the value of a*b*c*d (Posted on 2025-03-20)

If:

2^a = 3
3^b = 4
4^c = 5
5^d = 6

Then, find the value of a*b*c*d

No Solution Yet Submitted by K Sengupta

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Solution

| Comment 1 of 3

Take the logs of both sides of each equation and multiple the left and right sides:

a ln2 = ln3

b ln3 = ln4

c ln4 = ln5

d ln5 = ln6

abcd * ln2 * ln3 * ln4 * ln5 = ln3 * ln4 * ln5 * ln6

cancel common terms ln3, ln4, ln5:

abcd * ln2 = ln6

abcd = ln6 / ln2 = log2(6) = 1 + log2(3)

Posted by Paul on 2025-03-20 12:04:52

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