Question

Help please, try to explain it in steps for me if u can't that's fine, ty!

Answer 1

B

Explanation:

We are given that Expression One is:

`2\cdot 10^x`

And Expression Two is:

`4\cdot 10^(x+y)`

We are given that the value of Expression Two is 20,000 times greater than the value of Expression One. And we want to find the value of y. In other words:

`4\cdot 10^(x+y)=20000(2\cdot 10^x)`

We can divide both sides by four:

`10^(x+y)=10000\cdot 10^x`

Recall that:

`x^a\cdot x^b=x^(a+b)`

Therefore:

`10^x\cdot 10^y=10000\cdot 10^x`

Divide both sides by 10ˣ:

`10^y=10000`

Solve for y:

`\displaystyle y = \log_(10)10000 = 4`

Our answer is B.