Question

(CEPBJ) A equação 16.5^2x = 25.20^x, em que x ∈ IR, admite solução igual a
a. 2 e 1/2
.b. √2.
c. 1/2.
d. 2.
e. -2 e 2.

Answer 1

$16\cdot5^{2x}=25\cdot20^x\\\\2^4\cdot5^{2x}=5^2\cdot(2^2\cdot5)^x\\\\2^4\cdot5^{2x}=5^2\cdot2^{2x}\cdot5^x\\\\2^4\cdot5^{2x}=2^{2x}\cdot5^{x+2}\\\\\frac{2^4}{2^{2x}}=\frac{5^{x+2}}{5^{2x}}$

$2^{4-2x}=5^{x+2-2x}\\\\4-2x=x+2-2x\\\\4=x+2\\\\\boxed{x=2}$