Question

Solve 5-3^x=-40 round to the nearest ten-thousandth

Answer 1

x=3.4650

Explanation:

`5-3^x=-40`

Solve the equation for x

First make the exponent alone, Subtract 5 from both sides

`-3^x= -45`

Divide both sides by -1

`3^x=45`

To solve for x , we write the equation in log form

`x=b^y` can be written as
`y=log_b(x)` in log form

`3^x=45` can be written as
`log_3(45)= x`

So, x= 3.46497 (Round to nearest ten thousandth)

x=3.4650

Answer 2

5-3^x = -40

subtract 5 from each side to get

-3^x=-45

divide both sides by -1 to make them positive

3^x = 45

need to do the natural logarithm on both sides to remove the variable from the exponent

so ln(3^x) = ln(45)

use logarithm rule to move x out

x ln (3) = ln(45)

dive each term by ln(3) then simplify to get

ln(3)/ln(45)

so x = ln(3)/ln(45) which calculates out to 3.46497352

round off to ten thousandths is 3.4650