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

Question

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

1. log base3^x^logbase3^x=16

2. 11^2x-11^x+1=-18

3. log base4(x-1)+log base4(x+5)=2

4. log base10(x+80)-log base10(3x-59)=2

5. 2(Inx)^2+Inx^13=-15

6. log base5(x+2)+log base5(4-x)=1

7. 3^2x-5(3x)=24

Answer 1

Dear Vivian,

    Here is what you can do for number 3:

 

 1.  Use the log rule, Log A    + Log B  = Log (A*B).

 

Log₄ (X+1) + log₄ (X+5)=2          Rewrite with log rule

 

Log₄ ( (X+1) (X+5) =2              Remember that a logarithm is a type of exponent, so write it as one.

 

4² =(X+1)(X+5)                Simplify equation

 

2.     16 = X² + 1X +5X +5      Bring the 16 to the other side, so that you can solve for "X."

 

3.    0= X² + 1X +5X +5-16      Simplify the equation, and collect terms.

 

4.  0= X² + 6X -11    

 

I will let you finish the problem.  You can complete the square to solve for "X," or you can use the quadratic formula.

 

If I helped you, please give me a thumbs up.

                                                        Susan C.