document.write( "Question 670883: Use the Laws of Logarithms to expand the expression.
\n" ); document.write( "ln sqrt 9r^8s.... instead of a regular sqrt its a cubed root but its not a 3 its 4.Its the sqrrot sigh with a little 4 \n" ); document.write( "
Algebra.Com's Answer #417210 by Theo(13342)\"\" \"About 
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i believe you are looking for the natural log of root4(9r^8s)
\n" ); document.write( "root4 is equivalent to taking the fourth root of which is equivalent to raising to the 1/4 power, so we get:
\n" ); document.write( "ln ((9r^8s)^(1/4))
\n" ); document.write( "this becomes:
\n" ); document.write( "(1/4) * ln ((9r^8s) which becomes:
\n" ); document.write( "(1/4) * [ ln(9) + ln(r^8s) ] which becomes:
\n" ); document.write( "(1/4) * ln(9) + (1/4) * ln(r^8s) which becomes:
\n" ); document.write( "(1/4) * ln(9) + (1/4) * 8 * s * ln(r)
\n" ); document.write( "to confirm this was done correctly, i let r = 2 and s = 3 and i solved using both the original expression and the final expression and got the same answer of 4.70819 rounded to 5 decimal places.
\n" ); document.write( "the concepts you use are:
\n" ); document.write( "log(a^b) = b*log(a)
\n" ); document.write( "log((a^b)^c) = c*log(a^b) = b*c*log(a)
\n" ); document.write( "log(a*b) = log(a) + log(b)\r
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