find the exact solution to each of the following logarithmic equation.

Question

find the exact solution to each of the following logarithmic equation.
1. 11^2x-11^x+1=-18
2.4^2x+1-4^x+1=3

Answer 1

1.-----------

Say    11^x=y

 

y^2-11y+18=0

 

y=9

y=2

 

11^x=9

Taking log on both sides

x log (11)=log(9)

x=log(9)/log(11)

x=0.916

Other solution

11^x=2

Taking log on both sides

x log(11)=log(2)

x=log(2)/log(11)

x=0.289

 

You should try the second part yourself now, since all steps are same.