Find the values of x and y if you know that b^3x/b^2x=b^10 and b^2x * b^x/b^y=b^8. Explain how you found your answer.

Answer 1

I'm assuming b^3x means b^3x and not b³x. Parentheses could help clarify.

b^3x/b^2x=b¹⁰

b^3x-2x=b^x=b¹⁰

Since b^x and b¹⁰ have the same base, b, then we can equate the exponents.

x=10

b^2xb^x/b^y=b⁸

b^2x+x/b^y=b^2x+x-y=b⁸

Again, we can equate the exponents

3x-y=8

Solve for y

y=3x-8

Set x to 10, which was found above

y = 30-8 = 22