SOLUTION: slove algebraically log base 4 (x+41)- log base 4(2x-5)=2

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Question 63849: slove algebraically log base 4 (x+41)- log base 4(2x-5)=2
Found 2 solutions by funmath, rahman:
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
slove algebraically log base 4 (x+41)- log base 4(2x-5)=2
log base 4((x+41)/(2x-5))=2 because log(a)-log(b)=log(a/b) if the bases are the same.
%28x%2B41%29%2F%282x-5%29=4%5E2 because log base a (b)=x ==> a^x=b
%28x%2B41%29%2F%282x-5%29=16
%282x-5%29%28x%2B41%29%2F%282x-5%29=16%282x-5%29
x%2B41=32x-80
x-x%2B41=32x-x-80
41=31x-80
41%2B80=31x-80%2B80
121=31x
121%2F31=31x%2F31
121%2F31=x
Check:
log base 4 (121/31+41)-log base 4 (2(121/31)-5)=2
log base 4 (1392/31)-log base 4 (87/31)=2
log base 4 ((1392/31)/(87/31))=2
log base 4((1392/31)(31/87))=2
log base 4(1392/87)=2
log base 4 (16)=2
log base 4 (4^2)=2
2=2 We're right!!!
Happy Calculating!!!

Answer by rahman(247) About Me  (Show Source):
You can put this solution on YOUR website!
log base 4 (x+41)- log base 4(2x-5)=2
log base 4 (x+41)- log base 4(2x-5)=log base 4 (4^2)
log base 4 (x+41)- log base 4(2x-5)=log base 4 (16)
log base 4 %28x%2B41%29%2F%282x-5%29=log base 4 (16)
%28x%2B41%29%2F%282x-5%29=16
%28x%2B41%29=16%2A%282x-5%29
x%2B41=32x-80
80%2B41=32x-x
121=31x
31x=121
31x%2F31=121%2F31
x=121%2F31
Ok