Tuesday

January 27, 2015

January 27, 2015

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

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 4:41pmduplicate

- Math-LOGS -
**MathMate**, Monday, December 21, 2009 at 4:53pmTo 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 11:59am2nd 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)

**Answer this Question**

**Related Questions**

math - Logarithm!!! Select all of the following that are true statements: (a) ...

Math Help Please - Which of the following expressions is equal to log (x sqrt-y...

Trigonometry - This is a logs question If u=x/y^2, which expression is ...

TRig WIth LoGs help1!! - i have problem i can't solve and the book is no help.. ...

11th grade-Logs - log x = 1/2 (log a + Log b - log c) express x in terms of a,b,...

Mathematics - Prove that log a, log ar, log ar^2 is an a.p. Is the following ...

math(Please help) - 1) use the properties of logarithms to simplify the ...

math - write as a single logarithm: -2logbase3(1/x)+(1/3)logbase3(square root of...

mathematics -logs - which three statements are true? a) if x= -10^4 then log 10...

math - Q1:solve log(5)x-log(25)(x+10) = 0.5 Q2:If 2log(a)x=1+log(a) (7x-10a) ,...