SOLUTION: 3 to the power of 2x-5 then +7=12 Please help me solve for x, thanks.

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Question 1130839: 3 to the power of 2x-5 then +7=12
Please help me solve for x, thanks.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


3%5E%282x-5%29%2B7+=+12

Isolate the term containing the variable:

3%5E%282x-5%29+=+5

The variable is in an exponent, so take the log of both sides:

%282x-5%29%2Alog%283%29+=+log%285%29

Expand the expression on the left and isolate the term containing the variable:

2x%2Alog%283%29-5%2Alog%283%29+=+log%285%29
2x%2Alog%283%29+=+5%2Alog%283%29%2Blog%285%29

Solve for x:

x+=+%285%2Alog%283%29%2Blog%285%29%29%2F%282%2Alog%283%29%29

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question from student (about an unrelated problem):

Hello, I have a basic math question and I think the person who gave me the answer got offended. In the equation, K=100*20squared/8, how do you get 500. Isn't 20 squared 400 then divided by 8=50?

What happened to the "100"?

100*20squared/8 = 100*400/8 = 100*50 = 5000