Problem 871

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

e^x+11 = .

 

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 b^M = b^N, THEN M = N.

To solve the exponential equation e^x+11 = , first express both sides of the equation as a power of the same base.

e ^x+11  = 

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}.