SOLUTION: Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic express

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Question 1167037: Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions.


1/6[5ln (x + 6) - ln x - ln (x 2 - 8)]
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
my development of the solution is shown on the following worksheet.

here it is:



the solution relies on the following concepts.

d * ln(a) = ln(a^d)

ln(a) - ln(b) = ln(a/b)

ln(a/b) - ln(c) = ln((a/b)/c) = ln(a/(b*c))

if you bracket your expressions with 3 { symbols in a row before the expression and 3 } symbols in a row after the expression, then your original expression will look like this:

%281%2F6%29+%2A+%285+%2A+ln%28x+%2B+6%29+-+ln%28x%29+-+ln+%28x%5E2-8%29%29

and your final expression will look like this:

ln%28%28%28x%2B6%29%5E5%2F%28x%2A%28x%5E2-8%29%29%29%5E%281%2F6%29%29