24^{7}.75^{9}.40^{8}=2^{x}\cdot3^{y}.5^{z}\Rightarrowx+y+z=

AP ICET 2017 Shift 2 Paper

Question : 77 of 200

Marks: +1, -0

24^{7}.75^{9}.40^{8}=2^{x}⋅3^{y}.5^{z}⇒x+y+z=

Solution:

24^{7}.75^{9}.40^{8}=2^{x}.3^{y}.5^{z}

⇒(2^{3}.3)^{7}.(3.5^{2})^{9}.(2^{3}.5)^8=2^x.3^y.5^z

⇒2^{21}.3^{7}⋅3^{9}⋅5^{18}⋅2^{24}⋅5^{8}=2^{x}⋅3^{y}⋅5^{2}

⇒2^{21+24}⋅3^{7+9}⋅5^{18+8}=2^{π}⋅3^{5^{5}}⋅5^{2}

⇒2^{45}⋅3^{16}⋅5^{25}=2^{{x}}⋅3^{3^{5}}⋅5^{2}

∴x=45,{y}=16,{z}=26

∴x+y+{z}=45+16+26=87

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