Question 1063440: pls help me out found dis question in a txt book a logarithm simultaenous eqn
2logbasex of y+2logbase x of y=5 ;xy=27 Answer by rothauserc(4718) (Show Source):
You can put this solution on YOUR website! (2 * log(x) y) + (2 * log(x) y) = 5 and x * y = 7
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use the power rule log(b) (x^y) = y ∙ log(b) (x)
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log(x) y^2 + log(x) y^2 = 5
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use the product rule log(b) (x * y) = log(b) (x) + log(b) (y)
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log(x) y^4 = 5
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use definition of logarithm
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y^4 = x^5
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use y = 7 / x and substitute for y
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(7 / x)^4 = x^5
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2401 / x^4 = x^5
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x^9 = 2401
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x = 2401^(1/9) = 2.3746
y = 7 / 2.3746 = 2.9479
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check answers
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(2 * log(2.3746) 2.9479) + (2 * log(2.3746) 2.9479) = 5
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(2 * 1.25) + 2 * 1.25) = 5
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2.50 + 2.50 = 5
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5 = 5
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our answer checks
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