SOLUTION: ln (sqrt x-8)=5 ln x + ln (x+3)= 1 log (x-6)= log (2x+1) need step by step instructions on how to do each problem... please include answer as well. Thank you.

Question 177448: ln (sqrt x-8)=5

ln x + ln (x+3)= 1

log (x-6)= log (2x+1)

need step by step instructions on how to do each problem... please include answer as well. Thank you.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
1.

First note that , so:

Now use the rule that for any , any , and any , so: →

Now use the definition if and only if

So: → , which is the exact answer. Use your calculator to get a numerical approximation if that is what you need.

------------------------------------

First use the rule: The sum of the logs equals the log of the product, , so: .

Now use the definition if and only if , so:

→ →

Use the quadratic formula:

Again, if you need a numerical approximation, use your calculator.

--------------------------------

Use the rule: if and only if

So: . You should be able to handle the rest of this one on your own.

RELATED QUESTIONS
I need help, step by step on how to solve ln (x +7) + ln (x + 3) = ln... (answered by Fombitz)

please help - not sure how to solve when I end up with log fractions? ln(x)- ln(x+1) = (answered by longjonsilver)

Please show how to condense the following expressions: 2 log 9 + 5 log x + log 1/3 3... (answered by lwsshak3)

Solve: log base 4 (X) + Log base 8 (x) = 1 ln X/ln 4 + ln X/ln 8=1 2 ln X/2 ln 4 + ln... (answered by Fombitz)

Solve and give exact solutions: 15. log2(x+2)+ log2(x-2)=5 17. log(5)= 2-log(x)... (answered by josmiceli)

ln (x + 6) - ln 10 = ln(x-1) - ln 2 Can you please show me the steps on how to solve... (answered by stanbon)

Two ln problems I need help with. ln 3 - (ln x + ln 6) = ln x - ln 8 ln 3 + ln 2x = (answered by stanbon)

lnx+ln(x+8)=4 i need help on how to solve this step by... (answered by KMST)

Write as a single log: 2 ln 5 - 3 ln x + ln(x^2+1)... (answered by Alan3354)