We are doing logarithms in algebra...how would you solve 1500e^x=5000?

Question

..I think the answer will be with the "log" symbol...

Answer 1

Hey there!

Here's the answer.

1500e^x=5000 --> Write the problem.
e^x=10/3 --> Divide 1500 on both sides of the equation.
ln(e^x)=ln(10/3) --> Take the natural log of each side of the equation.
x=ln(10/3) --> Apply the exponential-logarithmic inverse properties i.e. ln(e^x)=x and e^ln(x)=x.

So the answer is ln(10/3) or it can be broken down into ln(10)-ln(3).

Hope it helps!

Answer 2

first thing you should realize is that the answer to a log is an exponent.

log10(100)=x 10 being the base should read what number should 10 be raised to to get 100? so the answer is 2.

now, there are certain properties if you have log10(10) what number do you have to raise 10 to get 10? the answer is one. so if you take the log with base x of x you will get 1.

second thing you should realize is that e=2.7 something something. e is just a number.

third thing you should know is that log base e of a number is the same thing as the natural log or ln .. so ln is a special case of log where the base is the number e.

fourth thing you should see is that you can do anything to an equation as long as you do it to both sides to keep it equal. So if you take the log of the left side, and the log of the right side it will still be the same equation.

so being as you have an e in this expression you should work with ln.

now, if you take the log of the left side you'll be left with
ln (1500*e^x)=ln 5000

there is another property of logs which says that in a log if there is an eponent you can bring it to the front, use this property on the left side. you'll be left with:
x ln(1500*e) = ln 5000

now you're trying to solve for x. So you want to keep that on one side, you're just multiplying x times the log of whatever, so you divide the log on both sides to get rid of it, the ones on the left side cancel giving you.

x= ln5000/ln(1500*e)

plug in calc.

Answer 3

1500e^x = 5000
e^x = 5000 / 1500
e^x = 50 / 15
e^x = 10 / 3
ln (e^x) = ln (10 / 3)
x ln e = ln (10 / 3)
x = ln (10 / 3)
x = 1.204

Answer 4

1500e^x=5000

divide both sides by 1500

e^x = 10/3

take the natural logarith of each side

ln(e^x) = ln (10/3)

ln (e^x) = x & ln (10/3) = ln 10 - ln 3

so,

x = ln (10) - ln (3)

x = 2.3026 - 1.0986

x = 1.204

Answer 5

1500e^x = 5000
e^x = 10/3
Use ln at both sides,
ln (e^x) = ln(10/3)
x ln e = ln 10 - ln 3

So x = ln 10 - ln 3

Answer 6

frm above,e^x=5000/1500=10/3,
taking log of both sides,
xloge=log(10/3),
thus u will find x.u can talk log w.th rspect to any basei.e.either e or 10

Answer 7

1500 e^x =5000
e^x =5000/1500
e^x=3.33333
log(e)e^x=log(e)3.33333
xlog(e)e=log(e)3.33333
x=log(e)3.333333 = 1.20...........
You might want to go to google groups sci.math and post any problem you have. The chaps there are just waiting to help...themselves and you. haha

Answer 8

you ought to use the log definitions... log(base8) 512 = log 512 / log 8 = log 2^9 / log 2^3 = 9*log2/3*log2 = 9/3 = 3 Or, because of the fact the an above poster reported, you may placed it into your calculator.

Answer 9

take natural log of both sides and in going to call it ln or you can call it log to the base e

ln(1500*e^x) = ln(5000)

we know ln(a^k) = k*ln(a)

x*ln(1500*e) = ln(5000) ~1.16

checking:

1500*e^1.16 ~ 5000 so its ok :)

we can also say that ln(ab) = ln(a)+ln(b)

x*ln(1500)=ln(5000)

x= ln(5000)/ln(1500)

Answer 10

e^x=5000/1500=3.333
x=ln(3.333)= 1.204