how do you simplify log(10^6x^2)?

Question

anonymous · Answer

Is this $log_{10}(10^{6x^2})$ ?

anonymous · Answer

no  its   log(10^6 *separate*x^2)

anonymous · Answer

Oh,  this requires a rule of logarithms which is:
$$log_a(bc)=log_a(b)+log_a(c)$$
So:
$$log_{10}(10^6*x^2)=log_{10}(10^6)+log_{10}(x^2)$$
We also know that:
$$log_a(\phantom{.}b^c\phantom{.})=c\phantom{.}log_a(b)$$
So we can simplify this a bit further:
$$\eqalign{log_{10}(10^6*x^2)&=log_{10}(10^6)+log_{10}(x^2) \
                                               &=6log_{10}(10)+2log_{10}(x) \
                                               &=6(1)+2log_{10}(x) \
                                               &=2log_{10}(x)+6}$$

anonymous · Answer

AAAAAAAND...That's about as far as one can take it I believe haha