Calculus
posted by Raj .
Find the inverse of each relation:
y = (0.5)^(x+2)
and
y = 3log base 2 (x3) + 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 x2. Can someone tell me why it would end up being x2 and help me with the second one too.
I agree with your first answer.
y = 3log base 2 (x3) + 2
y2 = log3 (x3)^3
take the log3 of each side..
log3 (y2)= (x3)^3
take the cube root of each side
1/3 log3 ((y2)) = x3
x= 1/3 log3 ((y2))+3 but 3 is log3 (27)
x= 1/3 log3( y2) + log2 (27)
= 1/3 log3 (27*(y3))
check that.
y=
the answer is y = (log_{0.5}x)  2
be careful where the bracket is.
for the second, after you interchange the x and y variables you would have
x = 3log_{2}(y3) + 2
x2 = log_{2}(y3)^3
(y3)^3 = 2^{y3}
y+3 = [2^{y3}]^(1/3)
y = [2^{y3}]^(1/3)  3
the exponent on 2 inside the square bracket in the last 3 lines should have been x2 instead of y3
I kept copyandpasting 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 logtobase 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)x2 = y
For the second one, Reiny, you're right.
Thanks all for the help.
Respond to this Question
Similar Questions

Review of Logs
I can't seem to get the answer to this; the answer key says log(base 8)6 Write as a single logarithm log(base 8)42log(base 8)3  log(base 8) 6 I'm hoping the key is wrong :) Thank you for your help! 
log graph
How do you graph y= log (base 5)(x)? The written question is: Sketch above equation by first describing the transformations performed on the equation y= log (base 5)(x) And what is the inverse function? 
log equation graph
How do you graph y= log (base 5)(x)? The written question is: Sketch above equation by first describing the transformations performed on the equation y= log (base 5)(x) And what is the inverse function? 
graphing
How do you graph y= log (base 5)(x)? The written question is: Sketch above equation by first describing the transformations performed on the equation y= log (base 5)(x) And what is the inverse function? 
PreCalculus
Laws of Logarithms Without using a calculator use the change of base rule to evaluate 1. a) log(subscript8)32(hint use base 2) =log(subscript2 32)/log(subscript2 8) = 5/3 b) log(subscript36)1296. This one doesnt even give you a hint, … 
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!! 
Trig
log base b 64  log base b 16 = log base 4 16 solve for the variable.. i got to the part as far as: (log 4/log b) = 2 now i m stuck at how i can isolate the b. plz help! 
Algebra 2
Explain the difference between log base b (mn) and ( log base b of m)(log base b of n). Are they equivalent? 
Algebra 2
I am trying to find the inverse of these functions. Can someone please check my answers and tell me how to do number 2? 
Advanced Functions/ Precalculus Log
1. Evaluate 4^(log base4 64) + 10^(log100) 2. Write 1+log(base2)x^3 as a single logarithm 3. Write log(base b)√(x^3 y z^6) 4. Solve log(base 2)xlog(base 2)6=log(base 2)5+2log(base 2)3 5. Solve 3^(2x) = 9(81^x) 6. Solve 3^(2x)=7^(3x1). …