Here are a few, note x>0 and y>0 and a&b not = 1 * log (xy) = log(x) + log(y) * log(x/y) = log(x) - log(y) * loga(x) = logb(x)*loga(b) * logb(bn) = n * log(xa) = a*log(x) * logb(b) = 1 * logb(1) = 0
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250(x) = 400,000 Use logs to base '10' Hence log250^(x) = log400,000 xlog250 = log 400,000 Notirce how the power (x) becomes the coefficient. This is oerfectly correct under 'log' rules. x = log 400,000 / log 250 (NOT log(250/400,000). x = 5.60206 / 2.39794 x = 2.33619689..... ~ 2.33619 to 5 d.p.
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Use logarithms to base '10. Hence log(10) a^(1/50) Fiftieth root) and log (10) a^(1/2) second root ( square root) Under the rules of logarithms we can re-write as [(1/50)log a] / [(1/2)log a] Cancel down by 'log a' hence (1/50) / ( 1/2) 1/50 X 2/1 = 2/50 = 1/25 the answer!!!!!!
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You calculate a log, you do not solve a log!