Question 46884
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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"
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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*log (5, (x)) - log (5, (4)) = log (5, (16))}}}
{{{log (5, (x^3)) - log (5, (4)) = log (5, (16))}}} ---- Applying {{{a*log (b, (c))}}} = {{{log (b, (c^a))}}} 
              {{{log (5, (x^3/4)) = log (5, (16))}}} ---- Applying {{{log (b, (c)) - log (b, (d)) = log (b, (c/d))}}}
                           {{{x^3/4 = 16}}} ---- If {{{log (b, (c)) = log (b, (d))}}}, then c = d
                           {{{x^3 = 64}}} ------ Cross-multiplying
                      {{{root(3, x^3) = root (3, 64)}}} --- Taking the CUBE ROOT of each side
                             x = 4</font></font></font></b></pre>