Let be a real number such that Then
125x=a√b. What are a and b?
We can start by factoring 125:
125 = 5^3
Therefore, we can rewrite the equation as follows:
5^3x = a√b
We can also rewrite the right-hand side of the equation as follows:
a√b = a^(1/2)b^(1/4)
Setting the powers of 5 equal on both sides of the equation, we get:
3 = a^(1/2)b^(1/4)
Squaring both sides of the equation, we get:
9 = ab^(1/2)
Therefore, a=9 and b=16.
In conclusion, a=9 and b=16.