Write the following as a single logarithm : show workinglog3(5) log5(12)

It seems like there might be a misunderstanding in your question. The operation between log3(5) and log5(12) is not specified. If you want to multiply, add, subtract, or divide these two logarithms, the approach would be different.

However, if you meant to multiply these two logarithms, here's how you can do it:

log3(5) * log5(12)

This can be simplified using the change of base formula, which states that logb(a) = logc(a) / logc(b).

So, we can change the base to 10 (as it's the most commonly used base):

log3(5) = log10(5) / log10(3)

log5(12) = log10(12) / log10(5)

Then, the multiplication of these two logarithms would be:

log3(5) * log5(12) = (log10(5) / log10(3)) * (log10(12) / log10(5))

The log10(5) in the numerator and denominator will cancel out:

= log10(12) / log10(3)

So, log3(5) * log5(12) is equivalent to log10(12) / log10(3) when written as a single logarithm.