algebra 2 my question is 1.) 9^2x=3^2x+4 also have 2 additional problems

Question

Slove the exponential equation equation.Check for extraneous solutions. Round the result to three decimal places if necessary. 1.) 9^2x=3^{^2x+4}   10.) 3e^x =2 19.)9^2x=3^2x+4 

Answer 1

I will comment on the first  & second question, only because the third one is a duplicate!

 

First, I believe that on the left side you should realize that 9 = 3².  Then the equation can be rewritten as

 

(3²)^2x = 3^(2x+4)

 

3^4x = 3^2x+4

 

So the exponents must be equal!  Therefore 4x = 2x + 4;  2x = 4;  x = 2.

 

# 10:  e^x = 2/3; now take natural logarithms...x = ln (2/3).  Easy!