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

Answer 2

ok,

can I just check the equation is it

1.

\[2 \log(4) - \log(3) + 2\log(x) - 4 = 0\]

or

2.

\[2 \log(4) - \log(3) + 2\log(x - 4) = 0\]

Answer 3

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 ]

Answer 4

@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.

Answer 5

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

Answer 6

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

Answer 7

makes sense to me