Can the product law of logarithms be used to evaluate log(-2) + log(-3)?
I know that a negative logarithm is undefined. However, the product law will give:
log(-2)(-3)
=log(6)
=.7782
Is this allowed? Thanks for your help.
What you did:
log[(-2)(-3)] = log(6)
is just fine
however you can not find log -2 or log -3
because they are undefined
remember
10^log x = x
10^(nothing we know of) = -2
No, the product law of logarithms cannot be used to evaluate log(-2) + log(-3). This is because logarithms are only defined for positive real numbers. When you have negative numbers or zero as the argument of a logarithm, it is undefined.
In this case, both -2 and -3 are negative numbers, so the sum of their logarithms does not have a valid mathematical interpretation. The product law of logarithms can only be used when multiplying the arguments of logarithms.
In summary, log(-2) + log(-3) cannot be evaluated. The result is undefined.