Question

If
${2}^{a} = {3}^{b} = {6}^{c } showthat \: \frac{1}{a} + \frac{1}{b} - \frac{1}{c} = 0$
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Answer 1

Question :- If 2^a = 3^b = 6^c then show that 1/a + 1/b - 1/c = 0 .

Solution :--

Let us assume that 2^a=3^b=6^c = k ( where k is any constant Number ).

So, we have now,

2^a = k

→ 2 = k^(1/a),

and,

3^a = k

→ 3 = k^(1/b)

and , similarly,

6= k^(1/c)

Now, we know that , 2*3 = 6

Putting all values we get,

→ [k^(1/a)] * [k^(1/b)] = k^(1/c)

using (a^m * a^n = a^(m+n) ) Now in LHS ,

→ k^(1/a +1/b)= k^(1/c)

Comparing now , we get,

→ 1/a +1/b = 1/c

or,

→ 1/a + 1/b - 1/c = 0 .

✪✪ Hence Proved ✪✪

Answer 2

Solution ...in the Attachment