Find possible solution to the equation given

Question

Find a solution to the equation e^x = 15 using an inverse function. Is it the only solution?

A solution is x = ___?

Is this the only solution? ___

Answer 1

e^x = 15

take natural logs of both sides

x = ln15

x = about 2.708050201...

the one and only solution. It's unique

e=about 2.71828

(2.71828)^2.70805 = about 14.999

y= f(x) =e^x = 15

e^x has an inverse function found by switching x and y, then solving for the new y

f^-1(x) = e^y = x

take natural logs

ln(e^y) = lnx

y=lnx

substitute 15 for x

y = lnx

y =ln15 = about 2.708050201...