Given log 3= x and log 5 =y Express radical 3/5 in terms of x and y.
1) 1/2x-y
2) 1/2(x-y)
3) 1/2xy
4) 2(x-y)
You must have meant
log (√(3/5)
= log 3^(1/2) - log 5^(1/2)
= (1/2)( log3 - log 5)
= (1/2)(x - y)
To express radical 3/5 in terms of x and y, we need to rewrite it using logarithmic notation.
First, recall that the square root of a number can be expressed as the number raised to the power of 1/2. Therefore, √3/5 = (3/5)^(1/2).
Now, let's use logarithmic notation to write the expression (3/5)^(1/2).
We know that log(m^n) = n*log(m).
Using this property, we can rewrite (3/5)^(1/2) as 10^(log((3/5)^(1/2))).
Since (3/5)^(1/2) is not a power of 10, we will need to use the change of base formula in logarithms.
The change of base formula states that log(base a)b = log(base c)b / log(base c)a.
Using the change of base formula, we can rewrite the expression as 10^(log(3/5) / log(10^(1/2))).
Now we need to substitute the values of log 3 and log 5 into the expression.
Given log 3 = x and log 5 = y, we can substitute these values into the expression as 10^(((1/2) * log(3))/log(10)).
Simplifying further, we have 10^(((1/2) * x)/1) or 10^(1/2 * x).
Therefore, radical 3/5 can be expressed as 10^(1/2 * x), which is equivalent to option 2) 1/2(x-y).