Respuesta :
Answer:
2
Step-by-step explanation:
[tex](\frac{3}{4})^6 \times (\frac{16}{9})^5=(\frac{4}{3})^{x+2}[/tex]
[tex]\frac{3^6}{4^6} \cdot \frac{16^5}{9^5}=\frac{4^{x+2}}{3^{x+2}}[/tex]
[tex]\frac{3^6}{4^6} \cdot \frac{(4^2)^5}{(3^2)^5}=\frac{4^{x+2}}{3^{x+2}}[/tex]
[tex]\frac{3^6}{4^6} \cdot \frac{4^{10}}{3^{10}}=\frac{4^{x+2}}{3^{x+2}}[/tex]
[tex]\frac{3^6}{3^{10}} \cdot \frac{4^{10}}{4^6}=\frac{4^{x+2}}{3^{x+2}}[/tex]
[tex]3^{-4} \cdot 4^{4}=4^{x+2}3^{-(x+2)}[/tex]
This implies
x+2=4
and
-(x+2)=-4.
x+2=4 implies x=2 since subtract 2 on both sides gives us x=2.
Solving -(x+2)=-4 should give us the same value.
Multiply both sides by -1:
x+2=4
It is the same equation as the other.
You will get x=2 either way.
Let's check:
[tex](\frac{3}{4})^6 \times (\frac{16}{9})^5=(\frac{4}{3})^{2+2}[/tex]
[tex](\frac{3}{4})^6 \times (\frac{16}{9})^5=(\frac{4}{3})^{4}[/tex]
Put both sides into your calculator and see if you get the same thing on both sides:
Left hand side gives 256/81.
Right hand side gives 256/81.
Both side are indeed the same for x=2.
