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Algebra 2 help please? And explanation too. Thanks!

  1. Solve the logarithmic equation. Round to the nearest ten-thousandth if necessary.

2 log 4 – log 3 + 2 log x – 4 = 0

12.3308

43.3013

86.6025

1,875

Verified Answer :

Answer:

The answer is: 43.3013

Step-by-step explanation:

we have to find the value of 'x' from the given equation

\(2 log 4-log 3+2 log x-4=0\\\\log4^{2}-log3+2 log x-4=0\)

since, we know that \(mlogn =logn^{m}\).

\(log16-log3+2logx-4=0\\\\log16-log3+2logx-4log10=0\\\\since, log10=1\\\\log16-log3+2logx-log10^{4}=0\\ \\log16-log3+2logx-log10000=0\)

also \(logm+logn=logmn\)

\(log16-log3-log10000+2logx=0\\\\log16-log3\times10000+2logx=0\\\\log16-log30000+2logx=0\)

since \(logm-logn=log\dfrac{m}{n}\)

\(log(\dfrac{16}{30000})=2logx\\ \\logx=\dfrac{log\dfrac{16}{30000} }{2}\\ \\x=43.3012701892251\)

x≈43.3013.




emilybrown0812

Answer:

B

Step-by-step explanation: