Question

Algebra 2 help please? And explanation too. Thanks!

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,

Answer 1

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.