Question 165154: Express as a single logarithm with a coeffiecient of 1:
2*log(x)- 2*log(y)+4*log(z)
Many thanks for helping!
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! you use two logarithmic relationships to get to this answer.
first relationship is log (a*b) = log(a) + log(b).
second relationship is log (a^b) = b*log(a).
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this is how it works in your equation.
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second relationship allows you to rewrite your equation as:
2*log(x) + 2*log(y) + 4*log(z) = log(x^2) + log(y^2) + log(z^4)
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first relationship allows you to rewrite your equation as:
log(x^2*y^2*z^4) ******************************************************
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that's your answer.
to prove it, let x, y, and z be any numbers chosen at random.
i chose:
x = 3
y = 7
z = 15
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2*log(3) + 2*log(7) + 4*log(15) = 7.348803626 ****************
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3^2 = 9
7^2 = 49
15^4 = 50625
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9*49*50625 = 22325625
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log(22325625) = 7.348803626 ******************
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answers match proving solution is correct.
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