1. ## Am I right?

Write the following expression as one logarithm:
2 logx - log4 - log3 + logx

My work:
logx^4 - log4/3
log (x^4) / (4/3)
log (3x^4/4)

I am not sure if this is correct because I was uncertain whether to multiply the -log4 and -log3 or divide them.

Thanks for any help.

2. Originally Posted by iluvmathbutitshard
Write the following expression as one logarithm:
2 logx - log4 - log3 + logx

My work:
logx^4 - log4/3
log (x^4) / (4/3)
log (3x^4/4)

I am not sure if this is correct because I was uncertain whether to multiply the -log4 and -log3 or divide them.

Thanks for any help.
hi
$2 \log x - \log 4 - \log 3 + \log x = 3\log x - (\log 4 + \log 3) = \log {x^3} - \log{12} = \log{\frac{x^3}{12}}$

3. Originally Posted by iluvmathbutitshard
Write the following expression as one logarithm:
2 logx - log4 - log3 + logx

My work:
logx^4 - log4/3
log (x^4) / (4/3)
log (3x^4/4)

I am not sure if this is correct because I was uncertain whether to multiply the -log4 and -log3 or divide them.

Thanks for any help.
$2 \log(x) - \log(4) - \log(3) + \log(x) =$ $\log(x^2) + \log(1/4) + \log(1/3) + \log(x) =\log(x^3/(4\times 3))$

CB