PreCalculus
posted by Caroline .
I'm having problems understanding how to do these problems.
25. 32^(2x3)=2
27. 1/4= 2^3x
29. 9^x=27
33. 81^(x1)= 27^2x

recall that log(x^a) = a * log x
25)
32^(2x3) = 2
take log of both sides to get
(2x3) log 32 = log 2
2x3 = log 2 / log 32
Now recall that loga/logb = log_b(a)
so, log2/log32 = log_32(2) = 1/5
since 2^5 = 32, 2 = 32^(1/5), so log_32(2) = 1/5
2x3 = 1/5
2x = 16/5
x = 8/5
Or, we could have started out by noting that 2 = 32^(1/5), so equating powers of 32,
2x3 = 1/5
...
27)
similarly, since 1/4 = 2^2,
2 = 3x
x = 2/3
29)
Since 3= 9^1/2, 27 = 3^3 = 9^3/2, so
x = 3/2
33)
27 = 3^3
81 = 3^4, so
27 = 81^(3/4)
equating powers,
x1 = 2x(3/4)
x1 = 3x/2
x/2 = 1
x = 2
check:
81^3 = 3^12
27^6 = 3^12
Respond to this Question
Similar Questions

PreCalculus
I am having trouble with several problems: 1) Find the coordinates of the center, foci, and the vertices, and the equations of the asymptotes of the graph of the equation (x+1)^2/2  y^2/8 =1 2) Write the standard form of the equation … 
PreCalculus
I am having trouble with several problems: 1) Find the coordinates of the center, foci, and the vertices, and the equations of the asymptotes of the graph of the equation (x+1)^2/2  y^2/8 =1 2) Write the standard form of the equation … 
PreCalculus
I am in Honors PreCalculus and am having a hard time understanding my teacher. I feel so stupid. Does anyone have any suggestions on a website that might give me some insight into what I am doing wrong? 
Math
I am having problems understanding how to solve problems like the following: a2 + b2 = c2 Please help me where I can understand solving problems such as the one above. 
Pre Algebra
I am having problems with inequality problems. The opposite of g is at least 5. Write an inequality and solve. 
Prealgebra
I have some practice problems, and I need to have them worked out, showing your work. I will gain a better understanding of these problems by practicing them. Thank you. (6x+1)(x^29x+5) (2x^4+3)(4x^3+2) (12y^3+8y^2+20y)divided 2y … 
Prealgebra
I have some practice problems, and I need to have them worked out, showing your work. I will gain a better understanding of these problems by practicing them. Thank you. (6x+1)(x^29x+5) (2x^4+3)(4x^3+2) (12y^3+8y^2+20y)divided 2y … 
pre calculus
Hi, I am having a problem trying to find and understanding how to find the extreme values. I have a problem which I can't do. Will someone please explain for me how to do it. I would like to be able to do other similar problems. This … 
pre calculus
Hi, I am having a problem trying to find and understanding how to find the extreme values. I have a problem which I can't do. Will someone please explain for me how to do it. I would like to be able to do other similar problems. This … 
algebra homework help
student missed 11 problems on a Chemistry test and received a grade of 65%. If all the problems were of equal value, how many problems were on the test?