SOLUTION: Solve for x: 2^(3x-1) = 4^(2x) I used logarithms to start this problem but I'm having trouble simplifying the problem. Here is what I have been able to do so far. log2^(3

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Solve for x: 2^(3x-1) = 4^(2x) I used logarithms to start this problem but I'm having trouble simplifying the problem. Here is what I have been able to do so far. log2^(3      Log On


   

Question 887532: Solve for x:
2^(3x-1) = 4^(2x)
I used logarithms to start this problem but I'm having trouble simplifying the problem. Here is what I have been able to do so far.
log2^(3x-1) = log4^(2x)
(3x-1)log2 = (2x)log4
(3x-1)= (2x)log4/log2
Found 2 solutions by josmiceli, MathTherapy:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Where you left off:
+3x+-+1+=+2x%2A%28+log%284%29+%2F+log%282%29+%29+
+3x+-+1+=+2x%2A%28+log%28+2%5E2+%29+%2F+log%282%29+%29+
+3x+-+1+=+2x%2A2%2A%28+log%282%29+%2F+log%282%29+%29+
+3x+-+1+=+2x%2A2%2A1+
+3x+-+1+=+4x+
+x+=+-1+
-------------
check:
+3x+-+1+=+2x%2A%28+log%284%29+%2F+log%282%29+%29+
+3%2A%28-1%29+-+1+=+2%2A%28-1%29%2A%28+log%284%29+%2F+log%282%29+%29+
+-3+-1+=+-2%2A%28+log%284%29+%2F+log%282%29+%29+
+%28+-4+%29+%2F+%28+-2+%29++=+%28+log%284%29+%2F+log%282%29+%29+
+2%2Alog%282%29++=+log%284%29+
+log%284%29+=+log%284%29+
OK

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Solve for x:
2^(3x-1) = 4^(2x)
I used logarithms to start this problem but I'm having trouble simplifying the problem. Here is what I have been able to do so far.
log2^(3x-1) = log4^(2x)
(3x-1)log2 = (2x)log4
(3x-1)= (2x)log4/log2


You could very well use logs, but it's so much easier to use exponents, and not nearly as confusing. Thus, we have:

2%5E%283x+-+1%29+=+4%5E%282x%29

2%5E%283x+-+1%29+=+%282%5E2%29%5E%282x%29 ------ Converting right-side to similar base: base 2

2%5E%283x+-+1%29+=+2%5E%284x%29

3x - 1 = 4x ----- Bases are equal, and so are their exponents

3x - 4x = 1

- x = 1

x+=+1%2F+-+1

highlight_green%28highlight_green%28x+=+-+1%29%29

You can do the check!! 



Send comments, “thank-yous,” and inquiries to “D” at MathMadEzy@aol.com.

Further help is available, online or in-person, for a fee, obviously. 



For FREE info and answers to questions about the ASVAB exam, the NYS 3 – 8 city/state wide exams,GENERAL

MATH and HOMEWORK QUESTIONS, or MATH QUESTIONS related to the Regents Integrated Algebra, 

Regents Geometry, Regents Algebra 2/Trigonometry, SHSAT, COOP/HSPT/TACHS, PSAT, SAT, ACT, SSAT/ISEE,

GRE, CLEP, and the TASC/GED, you can visit: http://asvabstudyzone.freeforums.net/.