SOLUTION: Hello, I was wondering if you could please help me evalute this logarithmic problem. I have a decent knowledge of the subject; however, I can am flustered by this problem. The i

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Hello, I was wondering if you could please help me evalute this logarithmic problem. I have a decent knowledge of the subject; however, I can am flustered by this problem. The i      Log On


   

Question 590442: Hello, I was wondering if you could please help me evalute this logarithmic problem. I have a decent knowledge of the subject; however, I can am flustered by this problem.
The instructions are "Solve the equation".
1/3(6)^(-4x)+1=6
Thank you for your time.
Found 2 solutions by Theo, scott8148:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
1/3(6)^(-4x)+1=6
i think your equation is this:
%281%2F3%29%2A%286%29%5E%28-4x%29%2B1+=+6

if so, then you would solve it as follows:

subtract 1 from both sides of the equation and then multiply both sides of the equation by 3 to get:

%286%29%5E%28-4x%29+=+15

take the log of both sides of this equation to get:

log%28%286%29%5E%28-4x%29%29+=+log%28%2815%29%29

since log(x^a) = a*log(x), this equation becomes:

-4x+%2A+log%28%286%29%29+=+log%28%2815%29%29

divide both sides of this equation by log%28%286%29%29 to get:

-4x+=+log%28%2815%29%29%2Flog%28%286%29%29

this becomes:

-4x = 1.511391594

divide both sides of this by -4 to get:

x = -.0377847899




Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
subtracting 1 ___ (1/3)(6)^(-4x) = 5

multiplying by 3 ___ 6^(-4x) = 15

taking log ___ (-4x) log(6) = log(15)

dividing by log(6) ___ -4x = log(15) / log(6)