SOLUTION: Solve the equation for x. ROUND your answer to TWO DECIMAL places, and do not include "x=" in your answer.. 5+8*ln x=25.8

Question 607251: Solve the equation for x. ROUND your answer to TWO DECIMAL places, and do not include "x=" in your answer..

5+8*ln x=25.8
Found 2 solutions by stanbon, jsmallt9:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
5+8*ln x=25.8
-----
8*ln(x) = 20.8
-----
ln(x) = 2.6
-----
x = e^2.6
-----
x = 13.48...
Cheers,
Stan H.
==============
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

Solving equations where the variable is in the argument (or base) of a logarithm usually starts by using algebra and/or log properties to transform the equation into one of the following forms:
log(expression) = other-expression
or
log(expression) = log(other-expression)

Your equation, with its single logarithm, should be transformed into the first form. This can be done quite simply. Subtract 5 from each side:

Then we divide both sides by 8:

which simplifies to

The next step. with the first form, is to rewrite the equation in exponential form. In general, is equivalent to . Using this pattern, and the fact that the base of ln is e, we get:

The next step is to solve for the variable. Your equation is already solved for the variable! All that is left, since a rounded decimal was requested, is to use your calculator:

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