Calculus

Find the inverse of each relation:

y = (0.5)^(x+2)
and
y = 3log base 2 (x-3) + 2

For the first one I got y=log base 0.5 (x+2)...but the answer in the back of the textbook says that it is not x+2, but x-2. Can someone tell me why it would end up being x-2 and help me with the second one too.

I agree with your first answer.

y = 3log base 2 (x-3) + 2
y-2 = log3 (x-3)^3
take the log3 of each side..

log3 (y-2)= (x-3)^3
take the cube root of each side
1/3 log3 ((y-2)) = x-3
x= 1/3 log3 ((y-2))+3 but 3 is log3 (27)
x= 1/3 log3( y-2) + log2 (27)
= 1/3 log3 (27*(y-3))

check that.
y=

the answer is y = (log0.5x) - 2

be careful where the bracket is.

for the second, after you interchange the x and y variables you would have
x = 3log2(y-3) + 2
x-2 = log2(y-3)^3

(y-3)^3 = 2y-3
y+3 = [2y-3]^(1/3)
y = [2y-3]^(1/3) - 3

the exponent on 2 inside the square bracket in the last 3 lines should have been x-2 instead of y-3

I kept copy-and-pasting so I kept copying my own typo.

If y is the x+2 power of 0.5, then you are correct. By definition, y is the log-to-base 0.5 of x+2

But they are asking for the inverse. What function of y is x?

(x+2) log 0.5 = log y (to any base)
x = [log y/log(0.5)] -2 (to any base)
= log(base0.5)y - 2

Yea, I figured out the first one.
y = (0.5)^(x+2)
x = (0.5)^(y+2)
log(base 0.5)x = y+2
log(base 0.5)x-2 = y

For the second one, Reiny, you're right.

Thanks all for the help.

  1. 0
  2. 0
  3. 10
asked by Raj

Respond to this Question

First Name

Your Response

Similar Questions

  1. Precalc

    1. 1/3log base 8 of (x+1)=2log base 8 of 3-(2/3)log base 8 of (x+1) 2. 2^x+8 times 2^=x all over 2 = 3 3. if log base a of 3= x and log base a of 2 = y, find each of thefollowing in terms of x and y log base a (18a^3) thanks!!

    asked by Rebekah on November 28, 2012
  2. Calculus

    Find the area cut off by x=4 from the hyperbola x^2/9-y^2/4=1. Answer is 4.982 in the book. I have proceeded as under: Y=2/3*sqrt(x^2-9) and rhe reqd. area is double of integral 2/3*sqrt(x^2-9) from 3 to 4. Int=

    asked by MS on March 28, 2014
  3. math

    indicates required items An operation * is defined by the relation x*y = 5x + 3y – 4xy. Evaluate [2*(-1) ] A. 15 B. 10 C. 8 D. -3 A B C D An operation * is defined by the relation x*y = 5x + 3y – 4xy. Evaluate (3*2)*4 A. -15

    asked by david dare on December 17, 2010
  4. math

    how do i solve this logarithm log(base 9)X + 3log(base 3)X = 14

    asked by kayla on January 8, 2009
  5. Math

    Does the relation in the table represent direct variation, inverse variation, or neither? If it is direct or inverse variation, write an equation to represent the relation. Explain your answer. x; 5,10,15,20 y; 2,1 ,2/3,1/2 Can

    asked by Olivia N J on March 1, 2017
  6. Algebra

    Find the inverse of the relation: {(0,1),(5,6),(-2,-4)}

    asked by Beth on July 20, 2009
  7. algebra

    what is the inverse of the given relation? for the function f(x)=xx-2,find (fof-1)(10)

    asked by zach on January 30, 2017
  8. Algebra 2

    How do I find the inverse of a linear relation represented by the points (2,4) (6,8) (-3,9) (-7,-8)?

    asked by Johnna on December 14, 2010
  9. Set theory

    consider the relation R=[(1,2),(2,5),(3.10),(4,17),(5,26)]. find the i)range ii)domain iii)inverse

    asked by Matrix School 2 on July 11, 2009
  10. Inverse of log function

    Find the inverse of f(x) = log(2+x) - 4 the base is "a" Call f(x) y y = loga(2+x) -4 y+4 = loga(2+x) a^(y+4) = 2 + x x = a^(y+4) - 2 drwls, you have merely solved the equation for x. The question was to find the "inverse", so the

    asked by Jen on March 1, 2007

More Similar Questions