Given that log 5=x and log -7 =y. Evaluate the following :
a) log x/y.
b) log xy.
What are the answers, I'm not understanding.
So x/y =0. Is it so.
as before,
log x/y = logx - logy
log xy = logx + logy
rather than just posting the same question again, spend some time reviewing logs.
To evaluate the expressions, we will use the basic properties of logarithms.
a) Evaluating log x/y:
We know that log x/y can be written as log x - log y using the quotient rule of logarithms.
Given that log 5 = x and log -7 = y, we can substitute these values into the expression as follows:
log x/y = log 5 - log -7
However, we cannot take the logarithm of a negative number, so we need to handle the second term separately. We can rewrite log -7 as log (-1 * 7) and apply the rules of logarithms to split it further:
log (-1 * 7) = log (-1) + log 7
Now, let's substitute the values of x and y:
log x/y = log 5 - (log (-1) + log 7)
Since log (-1) is not defined, we cannot simplify this expression any further. Therefore, the result is log x/y = log 5 - (log (-1) + log 7).
b) Evaluating log xy:
We can use the product rule of logarithms to evaluate this expression.
Given that log 5 = x and log -7 = y, we can substitute these values into the expression as follows:
log xy = log 5 + log -7
Again, we need to handle the term log -7 separately due to the negative sign. We can rewrite log -7 as log (-1 * 7) and apply the rules of logarithms to split it further:
log (-1 * 7) = log (-1) + log 7
Now, let's substitute the values of x and y:
log xy = log 5 + (log (-1) + log 7)
Since log (-1) is not defined, we cannot simplify this expression any further. Therefore, the result is log xy = log 5 + (log (-1) + log 7).