Answer:
x=6
Step-by-step explanation:
81^x = 27 ^(x+2)
81 = 3^4 and 27 =3^3 so replace 81 and 27 in the equation
3^4^x = 3^3^(x+2)
When we have a power to a power we can multiply the exponents
a ^b^c = a^(b*c)
3^(4x) = 3^(3*(x+2))
Since the bases are the same, the exponents have to be the same
a^b = a^c means b=c
4x = 3(x+2)
Now we can solve for x
Distribute
4x = 3x+6
Subtract 3x from each side
4x-3x = 3x-3x+6
x = 6
Work Shown:
x+x+90 = 180 .... all three angles of a triangle add to 180
2x+90 = 180
2x = 180-90
2x = 90
x = 90/2
x = 45
This is a 45-45-90 right triangle. We also consider it an isosceles right triangle because the base angles (45) are equal.
the answer should $201.25
