Homework Help: Math-LOGS

Posted by Jess on Monday, December 21, 2009 at 4:32pm.

Express x in terms of a,b and c.
log x = 1/2 (log a + log b - log c)
Please solve and explain how to do this type of problem, thank you!

Math-LOGS - Anonymous, Monday, December 21, 2009 at 4:41pm
duplicate
Math-LOGS - MathMate, Monday, December 21, 2009 at 4:53pm
To solve
log x = 1/2 (log a + log b - log c)
we need to know some properties of logarithms, namely:

1. log(a)+log(b) = log(ab)
2. (1/2)log(a)=log(a^-1/2)=log(√(a))
3. e^{ln x} = x, or
10^{log10 x} = x

Proceeding to simplify the right-hand-side,
log x = 1/2 (log a + log b - log c)
= (1/2)log a + (1/2)log b + (1/2)log c
= log(√a) + log(√b) + log(√c)
= log(√a √b √c)
= log(√(abc))

Assuming log() stands for logarithm to the base e,
e^{log x} = e^{log(√(abc))}
x = √(abc)
correction - MathMate, Tuesday, December 22, 2009 at 11:59am
2nd rule of logarithm should read:
2. (1/2)log(a)=log(a^1/2)=log(√(a))

and the solution has to be corrected because of an erroneous sign:

Proceeding to simplify the right-hand-side,
log x = 1/2 (log a + log b - log c)
= (1/2)log a + (1/2)log b - (1/2)log c
= log(√a) + log(√b) - log(√c)
= log(√a √b / √c)
= log(√(ab/c))

Assuming log() stands for logarithm to the base e,
e^{log x} = e^{log(√(ab/c))}
x = √(ab/c)

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