If x y z are integers such that 18^5* 40^3= 2^x*3^y*5^z ,then x+y+z
class 8 maths
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Answer: Factors of 18 and 40 are,
18= 2*3*3
40=2*2*2*5
18^5=(2^5)(3^5)(3^5) =(2^5)(3^10)
....3^(5+5)
40^3=(2^3)(2^3)(2^3)(5^3)
=(2^9)(5^3)
....2^(3+3+3)
(18^5)(40^3)=(2^5)(2^9)(3^10)(5^3)
=(2^14)(3^10)(5^3)
....2^(5+9)
Now, from above we get,
x=14, y=10 and z=3
Hence, x+y+z= 14+10+3= 27
Hope this is helpful.
18= 2*3*3
40=2*2*2*5
18^5=(2^5)(3^5)(3^5) =(2^5)(3^10)
....3^(5+5)
40^3=(2^3)(2^3)(2^3)(5^3)
=(2^9)(5^3)
....2^(3+3+3)
(18^5)(40^3)=(2^5)(2^9)(3^10)(5^3)
=(2^14)(3^10)(5^3)
....2^(5+9)
Now, from above we get,
x=14, y=10 and z=3
Hence, x+y+z= 14+10+3= 27
Hope this is helpful.
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