What does x equal if the equation is ln(3x+7)=3?

ln ( 3x+7 ) = 3

Taking anti log of both the sides we get ---

3x + 7 = e^3

=> 3 x = e^3 - 7

=> x = (1/3) [ e^3 - 7 ] .......... Answer

Or you may put the value of e^3 = 20.0855

=> x = (1/3) [20.0855 - 7]

=> x = (1/3) 13.0855

=> x = 4.3618..... Answer Answer


Dr. P.K.Tandon




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Dr P.K.Tandon has very correctly solved the problem.

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

The invese function of the natural logarithm ln(x) is the exponential function, exp(x) = e^x, where "e^x" is the "internet" way of writing "e raised to the power x," and "e" is the "natural" base, a non-terminating non-repeating number that is approximately e ~= 2.718281828459[...].

Since ln() and exp() are inverse functions of each other, exp(ln(x)) = x for all positive "x." (For negative "x," ln(x) is a complex number, not a real number, so while the identity exp(ln(x)) = x is still formally valid, the answer would not be considered acceptable unless one is doing complex rather than real analysis.)

Taking the exponential of both sides, subtracting 7 from both sides, and dividing both sides by 3 yields:

x = (1/3) * (exp(3) - 7);

therefore, x is approximately 4.361845641063[...].

Remember that a logarithm is just a fancy way of writing a problem involving exponents. So let's rewrite your problem using exponential notation:

e^3 = 3x + 7

Now just solve for x:

e^3 - 7 = 3x

(e^3 - 7) / 3 = x

So x = (e^3 - 7) / 3 ~ 4.36

(3x+7)=3
3x=-4
x=-1.333 (reacurring)

Hope this has helped =)

Could anyone help me with my pproblem?
http://uk.answers.yahoo.com/question/index;_ylt=Ag1ut63BBIMdEvSLccSy_4EgBgx.;_ylv=3?qid=20090117130924AAdtZWA

=)
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