Express As A Single Log

[mathxyz]

Express as a single log.

1) 8log_2 (sqrt{3x-2}) - log_2 (4/x) + log_2 (4)

2) 2(log_a (5x^3) - 1/2 log_a (2x + 3)

 

[happy]

Janet?

 

[pav]

loga-logb= log (a/b)

loga-logb+logc

log(a/b)*c

 

[mathxyz]

pav

Thank you so much for your help.
I have a test on Monday.

Jack

 

[Guest]

"Sandiego" ought to be two words.

 

[Matt]

Depends on how fast you say it. :wink:

 

[mathxyz]

No help

I will wait for someone else to reply with my log questions.

 

[mathxyz]

OKAY

MY WORK WITH QUESTION 2:

Is it right?

Express as a single log.

1) 8log_2 (sqrt{3x-2}) - log_2 (4/x) + log_2 (4)

2) 2(log_a (5x^3) - 1/2 log_a (2x + 3)

QUESTION 2:

log_a (5x^3)^2) - log_a (2x + 3)^1/2

log_a (5x^3)^2 - log_asqrt{2x + 3}

I now apply the difference of log rules.

My final answer for question 2:

log_a (5x^6/sqrt{2x + 3} )

Is it right?

Who can help me with question 1 stated above?

 

[tkhunny]

Question #2 - Sooooo Close. That '5' should be a '25'.

 

[Gene]

1) 8log_2 (sqrt{3x-2}) - log_2 (4/x) + log_2 (4) =
log_2((3x-2)^(1/2)^8) - log_2(4/x)+log_2(4) =
log_2((3x-2)^4) - log_2(4/x) + log_2(4) =
log_2((3x-2^4)*(x/4)*(4) =
log_2((3x-2)^4*x)

 

[mathxyz]

Great

I did not miss question 2 by much. Gene, thanks for your help with question 1. I get it now.