Use the log properties: LogA+logB=log(A*B) and log(A/B)=logA-logB.
ALso NlogA=log(A^N).
So 2log4=log4^2=log 16.
2logx=logx^2. Then we have log16-log3+logx^2-4=0.
Bring the 4 to the other side:
log16-log3+logx^2=4 Combine using the properties into one log:
log(16/3)*x^2=4.
With log, the understood base is 10. log _(10) [ (16/3)*(x^2]=4 where_10 means base 10.
We know log_b M=N means b^N=M by the definition of log. We use that here and change log into an exponential equation:
10^4=(16/3)x^2
10000 *(3/16)=x^2
Taking the square root we have + or- 43.30127.
We only want the positive solution since we can only take the log of positive numbers.
Our answer rounded is 43.3013.
