SOLUTION: How do you solve this logarithmic equation: log(4X+1)-log(2X-3)=2

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Question 143981: How do you solve this logarithmic equation: log(4X+1)-log(2X-3)=2
Found 2 solutions by jim_thompson5910, vleith:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
log%2810%2C%284x%2B1%29%29-log%2810%2C%282x-3%29%29=2 Start with the given equation


log%2810%2C%28%284x%2B1%29%2F%282x-3%29%29%29=2 Combine the logs using the identity log%28b%2C%28A%29%29-log%28b%2C%28B%29%29=log%28b%2C%28A%2FB%29%29


10%5E2=%284x%2B1%29%2F%282x-3%29 Rewrite the equation using the property: log%28b%2C%28x%29%29=y ====> b%5Ey=x


100=%284x%2B1%29%2F%282x-3%29 Square 10 to get 100


100%282x-3%29=4x%2B1 Multiply both sides by 2x-3


200x-300=4x%2B1 Distribute


200x=4x%2B1%2B300Add 300 to both sides


200x-4x=1%2B300 Subtract 4x from both sides


196x=1%2B300 Combine like terms on the left side


196x=301 Combine like terms on the right side


x=%28301%29%2F%28196%29 Divide both sides by 196 to isolate x



x=43%2F28 Reduce

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Answer:
So our answer is x=43%2F28 (which is approximately x=1.53571 in decimal form)


Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Given log%284X%2B1%29-log%282X-3%29=2+
log%28%284X%2B1%29%2F%282X-3%29%29=2+
10%5E%28+log%28%284X%2B1%29%2F%282X-3%29%29%29+=+10%5E2+
%284X%2B1%29%2F%282X-3%29+=+100+
%284X%2B1%29+=+200x+-+300+
301+=+196x+
301%2F196+=+x+
Plug that back in and check with a calculator