If 2^x =30 find 2^(x+3) A)8 B)5 C)240 D)200 E)250 (Good Luck! Plz solve fast!)

Question

asked Feb 24, 2021 115k views

2 Answers

Priyak Dey · Answer 1 · 2021-03-02T11:36:12+0000

Answer:

C

Explanation:

So we already know that:

2^x=30

And we want to find the value of:

2^(x+3)

So, what you want to do here is to separate the exponents. Recall the properties of exponents, where:

$x^2\cdot x^3=x^(2+3)=x^5$

We can do the reverse of this. In other words:

$2^(x+3)=2^x\cdot 2^3$

If we multiply it back together, we can check that this statement is true.

Thus, go back to the original equation and multiply both sides by 2^3:

$2^x(2^3)=30(2^3)\\$

Combine the left and multiply out the right. 2^3 is 8:

$2^(x+3)=30(8)\\2^(x+3)=240$

The answer is C.