## rosedewittbukater 2 years ago 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

1. matricked

use log a+log b=log ab and log a- log b= log (a/b)

2. campbell_st

ok, can I just check the equation is it 1. \[2 \log(4) - \log(3) + 2\log(x) - 4 = 0\] or 2. \[2 \log(4) - \log(3) + 2\log(x - 4) = 0\]

3. matricked

thus here we have 2 log 4 – log 3 + 2 log x – 4 =0 or log (4^2*x^2 )/3 = 4 [nlog a =log a^n] and log 1=10 as the base must be 10 here ]

4. rosedewittbukater

@campbell_st Honestly I'm not really sure. It's a question for my online school and it doesn't specify what it is, but I'm assuming it's (x-4). I guess we can know which it is if there's no answer choice.

5. matricked

2 log 4 – log 3 + 2 log x – 4 =0 log (4^2*x^2 )/3 = 4 log (4^2*x^2 )/3 =4 log 10 [as log10=1] log (4^2*x^2 )/3 = log 10000 or 16x^2/3 =10000 or x^2 =10000/16 *3 or x^2 =1875 hence x=sqrt(1875) =43.3013

6. matricked

@campbell_st u were right in interpreting the question but it is as it was

7. campbell_st

makes sense to me