Powerful power exponents

Algebra Level 2

Solve the equation :- 64. 9 x − 84.1 2 x + 27.1 6 x = 0 64.9^{x } -84.12^{x}+27.16^{x}=0 Note :- (.) stands for multiplication

3 and 4 1/2 and 1 2 and 3 1 and 2

Devkant Chouhan by Devkant Chouhan , 23, India

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2 solutions

Adiraju Uttej
Nov 14, 2014

the answer can be attained by substitution of options. answer: 1 and 2

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Bhanu Prasad
Nov 9, 2014

Divide 9^x on both sides then the equation becomes 64-84 (12%9)^x+27 (16%9)^x=64-84 (4%3)^x+27 (4%3)^2 Let (4%3)^x=t then; Eqn become. 27 t^2-84 t+64 it is quadratic equation in 't' solving we get t=4%3;t=16%9 As t=(4%3)^x then x=1,2

0 Helpful 1 Interesting 1 Brilliant 0 Confused

64-84(12%9)^x+27(16%9)^x=64-84(4%3)^x+27(4%3)^2 in this step how uyou got 27(16%9)^x as 27(4%3)^2

Amal Mohanan - 6 years, 7 months ago

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