The denominator of a fraction is 2 more than its numerator.

When 1/2 is added to this fraction, the resulting fraction's denominator is twice the denominator of the original fraction and its numerator is 1 more than its denominator.

What is the numerator of the original fraction?

3

5

8

11

My answer='A'

What is the exact solution to the equation e^3x+5=9?

x=3/5+ln9

x=3/ln9-5

x=5+ln9/3

x=ln9-5/3

My answer='C'

Guest Jan 17, 2018

#1**+1 **

The denominator of a fraction is 2 more than its numerator.

When 1/2 is added to this fraction, the resulting fraction's denominator is twice the denominator of the original fraction and its numerator is 1 more than its denominator.

What is the numerator of the original fraction?

We have

x / [ x + 2 ] + 1/2 = [ 2 (x + 2) + 1 ] / [ 2(x + 2) ]

Simplify

[ 2x + x + 2 ] / [2 (x + 2] = [ 2x + 5 ] / [ 2(x + 2) ]

Multiply through by 2(x + 2)

2x + x + 2 = 2x + 5

3x + 2 = 2x + 5

x = 3 ⇒ "A" is correct !!!!

I think this is.....

e^(3x+5) = 9 take the Ln of both sides

Ln e^(3x + 5) = Ln 9

(3x + 5) Ln e = Ln 9 ⇒ { Ln e = 1}

3x + 5 = Ln 9 subtract 5 from both sides

3x = Ln (9) - 5 divide both sides by 3

x = [ Ln (9) - 5 ] / 3 ......the last answer is correct....if I've interpreted this correctly

CPhill
Jan 17, 2018