Solve For X?

Question

a) e^(2x+3) - 7 = 0
b) ln(5-2x) = -3

Answer 1

a) e^(2x+3) = 7
LNe^(2x+3) = (2x+3)= LN7,
x = (LN7 - 3)/2

b) LN(5-2x) = -3
e^LN(5-2x) = (5 - 2x) = e^-3,
x = (5 - e^-3)/2

Answer 2

These questions are about the definition of natural logarithm: if e^x = a, then ln a = x and vice versa. So just plug in the definition:

a) e^(2x+3) - 7 = 0 so e^(2x+3) = 7
Apply the definition giving 2x+3 = ln 7, then solve for x

b) ln(5-2x) = -3, apply the definition giving 5-2x = e^(-3) and solve.

Answer 3

Question a)
2x + 3 = ln 7
2x = (ln 7) - 3
x = (1/2) (ln 7 - 3)
x = - 0.527

Question b)
5 - 2x = e^(-3)
2x = 5 - e^(-3)
x = (1/2) (5 - 1/e³)
x = 2 . 485 (to 3 decimal places)

Answer 4

it is easy, e is Euler's Number and ln is a logarithm with Euler's Number as its base, ln is called natural logarithm. The value of e is a real number that have the value approx. 2,7182818284590452353602874713527 (windows calculator)

in logarithm,
a^b = c
log(c of base a) = b

and ln is logarithm with base e.

e^(2x+3) - 7 = 0
can be changed into
e^(2x+3) = 7
ln(7) = 2x+3
1,9459101490553133051053527434432 = 2x +3
x = -0,52704492547234334744732362827841

In the same, but reversed way:
ln(5-2x) = -3
e^-3 = 5 - 2x
0,049787068367863942979342415650062 = 5 - 2x
x = 2,475106465816068028510328792175

calculation with e and ln almost always need to use a calculator, unless you could recite the value of e, which is approx. 2,7182818284590452353602874713527, usually you'll only need to recite at most 5 numbers behind the decimal point 2,71828

The value of e can also be calculated as lim((1 + 1/n)^n)

Answer 5

e^(2x+3) = 7
ln(e^(2x+3)) = ln(7)
2x + 3 = ln(7)
x = ln(7)/2 - 3/2

ln(5-2x) = -3
5-2x = e^-3
x =-e^-3/2 + 5/2

Answer 6

a) e^(2x + 3) = 7
2x + 3 = ln (7)

x = ½ (ln(7) -3)

b) 5 - 2x = e^(-3)

x = ½ (5 - e^(-3))

Answer 7

a) e^(2x+3)=7 => ln[e^(2x+3)]=ln(7) => ln "kills" "e", so...

2x+3=ln(7) => 2x=ln(7)-3 => x=(ln(7)-3)/2


b)ln(5-2x) = -3 => e^(ln(5-2x)) = e^(-3) => 5-2x=e^(-3)

2x=5-e^(-3) => x=(5-e^(-3))/2

Answer 8

2x+3=ln7
x=(ln7-3)/2


5-2x=e^(-3)
(5-e^(-3))/2=x

Answer 9

b ?