Question

Write each expression as a single logarithm.
log₇x+log₇y-log₇z

Answer 1

log₇(xy/z)

Explanation:

We know that

`\log_ax = b \implies a^b = x`

we also know that:

`a^b \cdot a^c = a^(b + c)`

so it follows that

`\log_ax + log_ay = log_a(xy)`

from:

`(a^b)/(a^c) = a^(b - c)`

follows that

`\log_ax - log_ay = log_a((x)/(y))`

so

`\log_7x + \log_7y - \log_7z = \log_7(xy) - \log_7z = \log_7((xy)/(z))`