1. To solve a logarithmic equation, rewrite the equation in exponential form and solve for the variable.
Problem 3: Solve for x in the equation
Answer: x=e-1 is the exact answer and x=1.71828182846 is an approximate answer.
Solution:
is the exact answer and
is an approximate answer.
Check: Let's substitute the approximate value x=1.71828182846 in the original equation and determine whether the left side of the equation equals the right side of the equation after the substitution. Remember we rounded the number and it is only a close approximation. Therefore, the left and right sides of the equation will most likely be very close but may not equal; it depends on the number of decimals you kept in the rounding process.
Since the value of the left side of the equation is 2 when you substitute
the value of x, and the right side of the equations is 2, you have proved
your answer.
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