Question 131451
I cannot figure out how to rewrite this logarithm as one simplified logarithm 
log(6x)+5log(3x)-3log(9x) 
Please help. 
<pre><font size = 4 color = "indigo"><b>
{{{log((6x))+5log((3x))-3log((9x))}}}

Use a rule of logs to write the coefficients as exponents:

{{{log((6x))+log((3x)^5)-log((9x)^3)}}}

Use a law of exponents to remove the inner parenthesesL:

{{{log((6x))+log((3^5x^5))-log((9^3x^3))}}}

Use a rule of logs on the first two terms:

{{{log((6x*3^5*x^5))-log((9^3x^3))}}}

Write {{{6}}} as {{{2*3}}} and {{{9}}} as {{{3^2}}}

{{{log((2*3*x*3^5*x^5))-log(((3^2)^3x^3))}}}

Add exponents of 3 and x in the first term and multiply
exponents in the second term:

{{{ log((2*3^6*x^6))-log((3^6x^3))}}}

Use a rule of logs:

{{{log(( (2*3^6*x^6)/(3^6x^3)  )     )}}}

 Cancel the {{{3^6}}}'s

{{{log(( (2*cross(3^6)*x^6)/(cross(3^6)x^3)  )     )}}}

{{{log(( (2*x^6)/(x^3)  )     )}}}

Subtract the exponents of the x's

{{{log( (2x^3)  )     }}}

Edwin</pre>