# Math-LOGS

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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 -

duplicate

• Math-LOGS -

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. eln x = x, or
10log10 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,
elog x = elog(√(abc))
x = √(abc)

• correction -

2nd rule of logarithm should read:
2. (1/2)log(a)=log(a1/2)=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,
elog x = elog(√(ab/c))
x = √(ab/c)