Question

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

Answer 1

Answer:

B

Step-by-step 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.