1) Use log_n(a xx b) = log_na + log_nblogn(a×b)=logna+lognb to seperate the expression into two logarithmic expressions.
= logx + log(x^3 + 9)^(-1/2)logx+log(x3+9)−12
2). Use loga^x = xlogalogax=xloga to get rid of the exponent.
Since the exponent is negative, we should first use the exponential property a^(-n) = 1/(a^n)a−n=1an
=logx + log(1/(x^3 + 9)^(1/2))logx+log(1(x3+9)12)
=logx + 1/2log(1/(x^3 + 9))logx+12log(1x3+9)
3). We now use the rule log_a(n/m) = log_an - log_amloga(nm)=logan−logam
=logx + 1/2(log1 - log(x^3 + 9))logx+12(log1−log(x3+9))
=logx + 1/2log1 - 1/2log(x^3 + 9)logx+12log1−12log(x3+9)
Since log1 = 0log1=0, we are left with logx - 1/2log(x^3 + 9)logx−12log(x3+9)
We could have just used the negative -1/2−12 at step 2, but I took the opportunity to show you an additional log rule.
Hopefully this helps!
