Question

If log6⁡⁡3+log6⁡⁡72=x, what is the value of x?

Answer 1

$\bf \textit{logarithm of factors}\\\\ log_{{ a}}(xy)\implies log_{{ a}}(x)+log_{{ a}}(y) \\\\\\ \textit{Logarithm Change of Base Rule}\\\\ log_{{ a}}{{ b}}\implies \cfrac{log_{{ c}}{{ b}}}{log_{{ c}}{{ a}}}\\\\ -------------------------------\\\\ log_6(3)+log_6(72)=x\implies log_6(3\cdot 72)=x\implies log_6(216)=x \\\\\\ \cfrac{log(216)}{log(6)}=x\impliedby \textit{using the change of base rule}$

recall that, log <--- with no apparent base, implies base10, so you can just plug that in your calculator

for the change of base rule, it doesn't really matter what base you use, so long is the same above and below, it just so happen, that we used base10 in this case, but could have been anything, same result.