How would I find..... see comments

Question

jpes2193 · Answer

$$\log_{7}42= $$

michele_laino · Answer

we can simplify your expression as follows:
$$\log _{7}42=\log _{7}7+\log _{7}6=1+\log _{7}6$$

jpes2193 · Answer

Ok and that should give you the same answer as the change of base formula?

michele_laino · Answer

yes I think so, since even if we change the base, the final result has to be the same

jpes2193 · Answer

okay so i would subtract the log7(6) and get log7(7)=1 
then what?

michele_laino · Answer

in order to get the result of your expression, we can compute log_7(6) using, for example, Windows calculator

jpes2193 · Answer

oh ok

michele_laino · Answer

sorry, we have to change the base of our logarithm from 7 to 10, first

jpes2193 · Answer

ahh see thats where you lost me. so Ill just stick with the change of base formula for this test...

michele_laino · Answer

in order to that, we can apply the subsequent formula:
$${\log _{10}}6 = \frac{{{{\log }_7}6}}{{{{\log }_7}10}}$$

michele_laino · Answer

sorry I gave you the wrong formula, here is the right formula:

michele_laino · Answer

$${\log _7}6 = \frac{{{{\log }_{10}}6}}{{{{\log }_{10}}7}}$$