Question

Solve:

7(2)^x=224

( help pls )

Answer 1

Answer: x = 5

Explanation:

`7(2)^x=224`

start by dividing 7 from both sides

`(7(2)^x)/(7) =(224)/(7)`

`2^x=32`

take the log of both sides

`log(2^x) = log(32)`

move the x to the left of the log

`xlog(2) = log(32)`

divide both sides by log(2)

`x=(log(32))/(log(2))`

use change-of-base formula

`(log(a))/(log(b)) =logx_(b) (a)`

`x = log_(2) (32)`

since
`2^5 = 32`, x = 5

Hope this helped :)

Answer 2

5

Explanation:

Original equation:

`7(2)^x=224`

Divide both sides by 7

`2^x=32`

Rewrite in log

`log_232=x`

You can do mental math to realize this equals 5, or plug this into your calculate (if it allows you to set the base), but if you can't do either, you can use the change of base formula:

`log_ba=(log (a))/(log(b))`

You get:

`log_232=(log(32))/(log(2))`

When you calculate using a calculator you should get 5