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Q.

For what value of x,   the equation 6 5 x 5 6 2x = 125 216   hold?


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a

2

b

3

c

4

d

5 

answer is B.

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Detailed Solution

The given equation is,
6 5 x 5 6 2x = 125 216  
Apply the following law of exponent:
a m ⋅ a n = a m+n  
⇒ 6 5 x 5 6 x 5 6 x = 5 6 3  
Apply the following law of exponent:
a m b m = (ab) m   ,
⇒ 6 5 × 5 6 x 5 6 x = 5 6 3   ⇒ 5 6 x = 5 6 3  
By comparing the exponents within the above equation, we obtain
x=3  
Therefore the value of x=3.   Hence option (2) is correct.
 
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