Condense the equation
log3+1/2logx-log5
log [ (3/5) sqrt x ]
remember log a - log b = log (a/b)
and
a log b = log b^a
To condense the given equation log3 + (1/2)logx - log5, we can simplify it by using logarithmic properties.
First, let's recall the properties of logarithms:
1. log(a) + log(b) = log(ab) -> We can combine logarithms with the same base by adding them.
2. log(a) - log(b) = log(a/b) -> We can subtract logarithms with the same base.
3. log(a^b) = b * log(a) -> We can bring the exponent as a coefficient in front of the logarithm.
Using these properties, let's condense the equation:
log3 + (1/2)logx - log5
Using property 1, we can combine the first two logarithms:
log(3x^(1/2)) - log5
Now, using property 2, we subtract the second logarithm:
log((3x^(1/2))/5)
Therefore, the condensed form of the equation log3 + (1/2)logx - log5 is log((3x^(1/2))/5).