Question

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

Answer 1

Answer:

x=3.4650

Step-by-step 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