Algebra 2 ? and explanation too. 5. solve the logarithmic equation. round to the nearest ten-thousandth if necessary. 2 log 4 – log 3 + 2 log x – 4 = 0 (1 point) 12.3308 43.3013 86.6025 1,875,

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.