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Yes, a physical quantity can have magnitude and direction but still be a scalar if it doesn't obey the vector addition. An example is Electric Current which has magnitude and a fixed direction, but it does not follow vector laws of addition.
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Log2aa=x then, a=(2a)x ......(1)
Log3a2a=y then,2a=(3a)y ......(2)
Log4a 3a=z then, 3a=(4a)z ......(3)
So,
a=(2a)x [from (1)]
Or, a=(3a)xy [from(2)]
Or, a=(4a)xyz [from(3)]
Multiplying both sides by 4a,
4a.a=4a.(4a)xyz
Or,(2a)² =(4a)xyz + 1
Or,(3a)2y =(4a)xyz+1
Or,(4a)2yz =(4a)xyz+1
Or, 2yz = xyz+1 .proved.
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very fine!
Glad to hear, miss!