# Thread: Needs help with LOG expressions! for algebra

1. ## LOG expression

write as a single logarithm: Ln5+2Lnx+4Ln(x^2+8)

Ln(_______)
i cant figure it out! i have trouble remembering what to do first

if anyone can help me with these it would be greatly appreciated!
thanks,

2. Originally Posted by bharriga
ln(a+b)+3 ln(a-b)-5 ln c

write as a single logarithm: ln ( )
cant figure it out! i have trouble remembering what to do first

also here is another similar problem:

Log(2)X+4 Log(2)y-3 Log(2)z

rewrite as single logarithm using this: Log2( )

if anyone can help me with these it would be greatly appreciated!
thanks,
Use the properties of the logarithm:

$\displaystyle \ln(a+b) +3 \ln(a-b) - 5\ln(c) = \ln(a+b) + \ln((a-b)^3) - \ln(c^5) = \ln\left(\frac{(a+b)(a-b)^3}{c^5}\right)$

$\displaystyle \log_2(x) + 4\log_2(y) - 3\log_2(z) = \log_2\left(\frac{x \cdot y^4}{z^3}\right)$

3. Originally Posted by bharriga
Ln(a+b)+3 Ln(a-b)-5 Ln c

write as a single logarithm: Ln (_______________)
cant figure it out! i have trouble remembering what to do first

also here is another similar problem:

Log(2)X+4 Log(2)y-3 Log(2)z

rewrite as single logarithm using this: Log2(________)

if anyone can help me with these it would be greatly appreciated!
thanks,

It doesn't matter what you do first as long as move the coefficients to exponents...

$\displaystyle \ln(a+b)+3 \ln(a-b)-5\ln(c)$

$\displaystyle \ln(a+b)+\ln((a-b)^3)-\ln(c^5)$

$\displaystyle \ln \left(\frac{(a+b)(a-b)^3}{c^5}\right)$

4. or do his method!

5. Originally Posted by bharriga
...
i cant figure it out! i have trouble remembering what to do first

...
Only in case you want to learn a little bit more about logarithms I've attached a pdf-file for you.