Question

Resolver a seguinte equação exponencial:
d) 3^x . 4^x = 5^x

Answer 1

$3^{x}\cdot4^{x}=5^{x}$

$\dfrac{3^{x}\cdot4^{x}}{5^{x}}=1$

Veja que, $3^{x}\cdot4^{x}=(3\cdot4)^{x}=12^{x}$.

Com isso, $\dfrac{12^{x}}{5^{x}}=1$.

Mas, $\dfrac{12^{x}}{5^{x}}=\left(\dfrac{12}{5}\right)^x$ e $1=\left(\dfrac{12}{5}\right)^0$.

Logo, $\left(\dfrac{12}{5}\right)^x=\left(\dfrac{12}{5}\right)^0$.

Portanto, $x=0$.