3^2x-5(3^x)=-6

Question

Using logarithms solve.

Answer 1

• (3^x)²-5(3^x)+6=0  ~  Writing it like this helps us see it as a variation of a traditional quadratic equation, which we can easily factor
• (3^x-2)(3^x-3)=0
• 3^x=2 OR 3^x=3 (two possible solutions at this point)
• 3^x=2
• xLn3=Ln2
• x=Ln2/Ln3 = .6309
• 3^x=3
• x=1

 

Therefore x=1 or .6309 (approx)