Answer:
B
Step-by-step explanation:
We are given that Expression One is:
[tex]2\cdot 10^x[/tex]
And Expression Two is:
[tex]4\cdot 10^{x+y}[/tex]
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:
[tex]4\cdot 10^{x+y}=20000(2\cdot 10^x)[/tex]
We can divide both sides by four:
[tex]10^{x+y}=10000\cdot 10^x[/tex]
Recall that:
[tex]x^a\cdot x^b=x^{a+b}[/tex]
Therefore:
[tex]10^x\cdot 10^y=10000\cdot 10^x[/tex]
Divide both sides by 10ˣ:
[tex]10^y=10000[/tex]
Solve for y:
[tex]\displaystyle y = \log_{10}10000 = 4[/tex]
Our answer is B.
