Question 897068: 4e^9x=560 find the solution in terms of natural logarithms? I don't understand how to solve because in examples I've seen the logs are in the equation
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 4e^9x=560
rewrite as 4 * e^(9x) = 560
divide both sides of the equation by 4 to get:
e^(9x) = 560 / 4
simplify to get:
e^(9x) = 140
take the natural log of both sides of the equation to get:
ln(e^(9x)) = ln(140)
since ln(e^(9x)) equals 9x * ln(e), your equation becomes:
9x * ln(e) = ln(140)
since ln(e) = 1, your equation becomes:
9x = ln(140)
divide both sides of the equation by 9 to get:
x = ln(140)/9
solve for x to get x = .5490713803...
go back to the original equation and replace x with that value to get:
4*e^(9x) = 4*e^(9*.5490713803...) = 4*e^(4.941642423) = 4*140 = 560
value for x is good.
you had 3 ways to solve this.
one was to take natural log of both sides of the equation as we did.
two was to take regular log of both sides of the equation.
three was to look at the equation of e^(9x) = 140 and use the basic definition of logs to transform it into a logarithmic equation as follows:
e^(9x) = 140 if and only if loge(140) = 9x
since loge is natural log shown as ln, the equation becomes ln(140) = 9x
divide both sides of the equation by 9 to get x = ln(140)/9 as we got before by taking the natural log of both sides of the equation.
any one of the three ways will get you the same answer.
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