log x = 1/2 (log a + Log b - log c)
express x in terms of a,b,and c.
See:
http://www.jiskha.com/display.cgi?id=1261431162
1+log 5 a - logo b - logo c
To express x in terms of a, b, and c, we can start by applying the properties of logarithms to simplify the given equation.
1. Begin by using the rule of logarithms:
log(xy) = logx + logy
log(x/a) = log(x) - log(a)
log(x/b) = log(x) - log(b)
log(x/c) = log(x) - log(c)
2. Apply the properties of logarithms to the given equation:
log(x) = 1/2 (log(a) + log(b) - log(c))
3. Multiply through by 2 to eliminate the fraction:
2 * log(x) = log(a) + log(b) - log(c)
4. Combine the logarithms on the right side:
2 * log(x) = log(ab) - log(c)
5. Use the rule of logarithms to simplify further:
2 * log(x) = log(ab/c)
6. Apply the exponential form of logarithms to get rid of the logarithms:
x^2 = ab/c
7. Finally, solve for x by taking the square root of both sides:
x = sqrt(ab/c)
Therefore, x can be expressed in terms of a, b, and c as x = sqrt(ab/c).
loga + logb - logc
log(ab/c)
z log q= log(q^z)
does that help?