SOLUTION: Solve the equation 3log5 x - log5 4 = log5 16

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Question 46884: Solve the equation 3log5 x - log5 4 = log5 16
Found 2 solutions by consc198, MathTherapy:
Answer by consc198(59) About Me  (Show Source):
You can put this solution on YOUR website!
3log5 x - log5 x 4 = log5 x 16
2.096910013 x -0.698970004 x 4 = 0.698970004 x 16
2.096910013 x -2.795880016 = 11.18352006
-5.862708801 = 11.18352006
11.18352006 + 5.862708801
Answer = 17.04622886

Answer by MathTherapy(10837) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the equation 3log5 x - log5 4 = log5 16
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Everything that the other person, consc198(59), did, was WRONG. He/she contends that:
"3log5 x - log5 x 4 = log5 x 16
2.096910013 x -0.698970004 x 4 = 0.698970004 x 16
2.096910013 x -2.795880016 = 11.18352006
-5.862708801 = 11.18352006
11.18352006 + 5.862708801
Answer = 17.04622886"
*******
This is CERTAINLY NOT the way to solve a LOGARITHMIC equation. Furthermore, the answer is
CERTAINLY NOT 17.04622886. Instead, it's done PRECISELY as follows:
3%2Alog+%285%2C+%28x%29%29+-+log+%285%2C+%284%29%29+=+log+%285%2C+%2816%29%29
log+%285%2C+%28x%5E3%29%29+-+log+%285%2C+%284%29%29+=+log+%285%2C+%2816%29%29 ---- Applying a%2Alog+%28b%2C+%28c%29%29 = log+%28b%2C+%28c%5Ea%29%29 
              log+%285%2C+%28x%5E3%2F4%29%29+=+log+%285%2C+%2816%29%29 ---- Applying log+%28b%2C+%28c%29%29+-+log+%28b%2C+%28d%29%29+=+log+%28b%2C+%28c%2Fd%29%29
                           x%5E3%2F4+=+16 ---- If log+%28b%2C+%28c%29%29+=+log+%28b%2C+%28d%29%29, then c = d
                           x%5E3+=+64 ------ Cross-multiplying
                      root%283%2C+x%5E3%29+=+root+%283%2C+64%29 --- Taking the CUBE ROOT of each side
                             x = 4