Assume that x is a positive number.?

Question

Assume that x is a positive number. Use the logarithm properties to present the expression log(x + 7) - log x as the logarithm of a single quantity.

Answer 1

log(x + 7) - log(x)

Here are three log properties that come into play for questions like these.

log[base b](a) + log[base b])(c) = log[base b](ac)
log[base b](a) - log[base b])(c) = log[base b](a/c)
log[base b](a^c) = c log[base b](a)

In our case, only the first second one will come into play.

log(x + 7) - log(x) = log [ (x + 7) / x ]

Answer 2

Simple log property:

log a - log b = log (a/b)

So
log(x+7) - log x = log ((x+7)/x) or log(1 + 7/x)