Question

Find the value of x if you know thatB* xb2 = 610 and = 691

Answer 1

We are asked to find the value of x given the following:

`(b^xb^2)/(b^4)=b^(10)`

and

`(b^x)/(b^y)=b^9`

From the first expression, and using the properties of powers of the same base, we can say:

x + 2 - 4 = 10

since the powers in the numerator will add, and that in the denominator will subtract.

then we solve for x :

x - 2 = 10

add 2 to both sides:

x = 10 + 2

x = 12

Knowing this, we can also answer what the value of "y" is from the second expression.

Using the properties of powers of the same base, in the second equation we know that

x - y = 9

since the power x is in the numerator and the power y in the denominator.

We know x from the first step (x = 12)

so we replace it to obtain "y"

12 - y = 9

add "y" to both sides:

12 = 9 + y

subtract 9 from both sides

12- 9 = y

y = 3