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
12.3308
43.3013
86.6025
1,875

Answer 1

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.

Answer 2

Answer:

B

Step-by-step explanation: