Question 194623: i dont understand how to express a prob;em in terms of sums and differences of logarithms . I need help with this ln of the fourth root of ab squared and i need help expressing 3 log base b of x-4logbaseb y+ (1/2)log base b of Z
Answer by RAY100(1637)   (Show Source):
You can put this solution on YOUR website! Some basis log relationships might help:
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log (ab) = log a + log b
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log (a/b) = log a - log b
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log a^b = b * log a
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try these by substituting simple numbers.
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problem (1) ,,,,ln ( (ab^2) )^.25,,,for exponents (c^2)^3 = c ^ (2*3) =c^6,,,,ab^(2*.25) = ab^.5
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ln ( (ab)^.5 ) = .5 lnab,,,,,,ANSWER
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check by evaluating original and answer with ab=10, both give 1.15,,,ok
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problem(2),,,, 3 log x -4 log y +1/2 log z,,,,,all logs to base b
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using above info,,,logx^3 -logy^4 +log z^.5
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using above info ,,,, log { (x^3 * z^.5)/ y^4}
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insetting base,,,,, log of base b { (x^3*z^.5)/y^4}
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check by substituting, arbitrarily, a=1, b=2,,c=3,,,into both original and answer
using just log to base 10,,, both give -.966,,,,,ok
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just work with simple problems for logs until it makes sense
keep up good work
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