Help ? Logs

Question

What is the inverse of y=(1/2)^x

---------------------------------------

find the given logarithm w/out using log function on calculator

1) log₁₀sqrt3

-------------------------------------

F(x)=log(x-3)

2)what are the x and y intercepts

3)domain and range

4)how does it compare to y=log(x)

------------------------------------

write equivalent logarithmic or exponential equations

5) ln0.5=-0.69

6) 0.37=e^(-1)

7) e⁰=1

 

Answer 1

Y = 1/2 ^X 

 

X = log_1/2 Y

 

1) log √3 = 1/2 log 3    / you should get log 3 from calculator

 

2)  f(x ) = log ( x -3) 

 

    X intercept:

 

       0 = log ( X-3)

 

       then:

      X -3 = 1    X =4

 

  Y - intercept:

 

     f(x) = log( 0- 3) / log -3  undefined

 

      No Y - intercept.

 

 

     3) Domain X -3 > 0     X > 3

 

          range ( -∞ , +∞) 

 

      4) graph of log( X-3) shifts log (X ) 3 units to the right.

 

      5)

 

          ln 0.5 = 0.69

 

             0.5 = e ^0.69

 

       6)

           0.37 = e ^-1

 

            -1 = ln 0.37

 

       7)  e⁰ =1

 

            ln 1 = 0