Problem 871

Solve the following exponential equation by expressing each side as a power of the same base and then equating exponents.

ex+11 = \frac{1}{e}.

 

Solution:-

 

An exponential equation is an equation containing a various in an exponent. Some exponential equations can be solved by expressing each side of the equation as a power of the same base.

All exponential functions are one-to-one. That is, two different ordered pairs have the same second component. Thus, if is a positive number other than 1 and bM = bN, THEN M = N.

To solve the exponential equation ex+11 =\frac{1}{e} , first express both sides of the equation as a power of the same base.

e x+11  = \frac{1}{e}

e x+11  = e-1

Then, set the exponents equal to each other and solve for x.

x + 11 = -1

x = -12

Therefore, the solution set is {-12}.

Leave a Reply

Your email address will not be published. Required fields are marked *