Question 1035219: Logarithmic Equation. What is the solution set of the function
log(base 5) x + log(base 5) (4x+1)= 1. Pls. Found 3 solutions by stanbon, nerdybill, MathTherapy:Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website! log(base 5) x + log(base 5) (4x+1)= 1
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log5[x(4x+1)] = 1
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4x^2+4x = 5
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4x^2 + 4x - 5 = 0
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x = [-4 +- sqrt(16-4*4*-5)]/8
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x = [-4 +- sqrt(96)]/8
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x = [-4 +- 4sqrt(6)]/8
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Positive solution::
x = [-4+4*sqrt(6)]/8 = 0.7247
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Cheers,
Stan H.
------------ Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website! log(base 5) x + log(base 5) (4x+1)= 1
log(base 5) [x(4x+1)] = 1
x(4x+1) = 5^1
4x^2+x = 5
4x^2+x-5 = 0
factoring:
(4x+5)(x-1) = 0
x = {-5/4, 1}
throw out the neg solution (extraneous) leaving:
x = 1