# Can someone help me solve for x? (Exponential Equation)

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#50/(1 +e^-x) = 4#

##### 2 Answers

#### Explanation:

Given:

#50/(1+e^(-x)) = 4#

Multiply both sides by

#50 = 4+4e^(-x)#

Subtract

#46 = e^(-x)#

Take natural logs of both sides to get:

#ln 46 = -x#

Multiply both sides by

#-ln 46 = x#

That is:

#x = -ln 46#

(which is the same as

#### Explanation:

#color(blue)"cross-multiply"# the equation.

#rArr4(1+e^-x)=50#

#"divide both sides by 4"#

#(cancel(4)(1+e^-x))/cancel(4)=50/4#

#rArr1+e^-x=12.5#

#"subtract 1 from both sides"#

#cancel(1)cancel(-1)+e^-x=12.5-1#

#rArre^-x=11.5#

#"using "color(blue)"law of logarithms"#

#color(red)(bar(ul(|color(white)(2/2)color(black)(logx^nhArrnlogx)color(white)(2/2)|)))#

#"take ln (natural log ) of both sides"#

#lne^-x=ln11.5#

#rArr-xcancel(lne)^1=ln11.5#

#rArrx=-ln11.5#

#rArrx~~-2.44" to 2 dec. places"#