How do I solve: e^(x+1)=4 , when solving for x?

Question

I just don't really understand the concept of e fully.

Answer 1

e^(x + 1) = 4

Take the natural log (ln) of both sides. When you take the natural log of e ^ (something), you eliminate the "e" and all you are left with is the exponent.

ln [e^ (x + 1) ] = ln [4]
x + 1 = ln [4]
x = ln [4] -1
x = 0.386

"e" isn't anything to be scared of; it's just another physical constant. Pi is 3.14.... "e" is 2.718....

It's also helpful to know that the natural log of "e" is 1.

Good luck.

Answer 2

Take a natural logarithm on both sides, that will cancel out the e. Now the question becomes x+1 = ln(4). This is much easier to solve..

Therefore x = ln(4)-1

Answer 3

The natural log of x (lnx) is the inverse of the function e^x

So

take the ln of both sides

ln(e^(x+1)) = ln4

x+1 = ln4

x = ln4 - 1

If you don't understand this yet you might want to look at the previous lessons in the book. It is best to grasp log base 10 before moving on to base e. Base 10 is more intuitive.

Answer 4

e^(x+1)=4
=> x + 1 = ln 4
=> x = ln 4 - 1 = 0.3863 (using calculator)

Answer 5

tanx=-4sinx sinx/cosx = -4sin sinx = -4 sinx cosx cos x = sinx/-4sin x = -a million/4 x= arccos (-a million/4) = 104.40 8 tiers csc²x=7tan(ninety° - x) - 11 Sorry, can no longer seem to discern this one out 5sin(ninety° - x) = sinx 5(-cosx) = sinx -5 = sinx/cosx = tanx x = arctan(-5) = -seventy 8.sixty 9 tiers 6cos²x=7-5sin x 6(a million-sin^2x) = 7-5sinx 6 - 6sin^x = 7 - 5sinx 6sin^2x -5sinx + a million = 0 sinx = [5 +/- sqrt(25-24)]12 sinx = 5/12 +/- a million/12 = a million/2 or a million/3 x arcsin (a million/2) = 30 tiers, or x = arcsin (a million/3) = 19.40 seven tiers

Answer 6

Take ln of both sides:-
(x + 1) ln e = ln 4
x + 1 = ln 4
x = (ln 4) - 1
x = 0.386

e is a special number whose value is approx. 2.718.
The important point to notice is that ln e = 1
Don`t worry about it otherwise.

Answer 7

take natural log of both sides, which is just the inverse of the e^ function.

so ln(e^(x+1)) = x+1

so we have x+1 = ln(4)

or x = ln(4) -1

Answer 8

take the natural log to get rid of the e
ln e^(x+1)=ln 4
x+1= ln 4
x= ln (4) - 1

Answer 9

e^x=exp (x)

exp(x)=y same as ln y = x

therefore exp(ln x) = x and ln(exp x) = x

e^(ln x) = x x greater than zero
ln(e^x) = x for all x


start by taking ln of both sides to get
x+1 = ln 4
then subtract 1 from both sides to get
x=(ln 4) - 1

Answer 10

Sorry but Einstein is dead! Here's a tip from the next best thing. My view on it is energy over an area (x) + 1 (dimension more) equals 4 i.e. the fourth dimension - gosh, I'm a genius! Who needs Einzwei?